I have been thinking of writing an article on market changes in the light of new events that did not surfaced until late end of January. Two issues come to my mind. Firstly, uprising in Middle East and second one is catastrophe in Japan.
http://graphics.thomsonreuters.com/11/03/GLB_KEY0311_SB.html
Uprisings in Middle East have created new uncertainty. In my mind what is happening in Middle East has parallels to catastrophe created by continental plate displacement in pacific basin. Uprisings have hit Tunisia, Egypt, Bahrain, Saudi Arabia and Libya. All these countries are being ruled by autocratic regimes for decades. This has created societies with rancor for government due to lack of political freedom and opportunities to survive. As old adage goes demography is destiny, populations were rising in these countries and have attained a critical mass where they can cause displacement of the existing regimes by venting their frustration. In the case of Tunisia and Egypt regimes were overturned. In other countries the process is progress and time will tell when it has happened. These events are shaping the course of world financial markets.
Catastrophe in Japan is another event that is shaping financial markets course. Scientists have put together tomes of research on plate tectonics and what happens in their wake in computer simulations. This is like trading on a practice account. Continental plates in pacific basin near North Japan have shifted and resulted in huge release of energy leading to Tsunami and earth quakes along the coast line of Japan. Japanese people have learnt from past experiences how to protect them from tsunami and earth quakes. But this time tsunami and earth quake have hit the nuclear power facilities and creating a catastrophe beyond imagination. This has set alarm bell around the world to review their existing procedures for safety in place. Japan will come out of this catastrophe with a big lesson for the rest of the world in terms of how to create a better nuclear facility.
I will go over various markets and how they were affected by these events,
US 10y treasury: 10 year treasury rates have stated their journey this year at around 3.30 %. At this time markets were pricing QE2 exit, housing recovery and EM world driven growth. Treasuries were literally in range bound market. I guess treasury markets needed a kick and Egypt uprisings have answered the call. But instead of safe haven bid treasuries shrugged this event and went on rising path. But Libya’s eccentric Gaddaffi put break to this rise in rates and brought international focus to Middle East. Infact this created uncertainty in oil markets and this got transmitted to other markets. This is difference between an eccentric Gaddaffi and suave Mubarak. Some times it pays to be eccentric. As this crisis in Libya is playing out between forces loyal to the ruling regime and rebels treasuries were grinding down. After this Treasuries were finding a level or were ignoring the crisis in Libya and started to rise. Another hurdle came in the form of Japan. This brought this market to high of 3.55 to 3.28 level, same as where we have started the year.
S&P 500 : US Equity markets, have started year at 1257 and were marching higher despite uprisings in Middle East. At the time of crisis in Libya SPX has received 1330. Looks very impressive testimonial for Federal Reserve’s new mandate to prop the stock market when they are in doldrums. But after that markets volatility increased and started moving around aimlessly. Finally tsunami brought bears out of hibernation to settle market at 1257.
VIX: VIX is a measure of volatility in the stock market and this has been falling for a while and remaining in range bound levels. Libya’s crisis brought in volatility and crisis in Japan and Bahrain elevated volatility to highs of 30.
Nikkei 225: Japanese Equity markets have been least correlated to these global events. But they have entered into downslide from the levels where it has started the year after the nature’s wrath fell on Japan.
Oil: Oil markets were on the rise since end of last year. This has been the response across all commodity markets due to fed’s loose monetary policy. Prices of everything are going up. Producers were able to pass the price increases to their customers. Recently at a Taco bell in Texas an angry customer fired his gun for price 50 % price rise on his beef tacos.
Gold : Gold has fell from historical highs to rise again as crisis is erupted in Middle East and Japan.
Monday, March 21, 2011
Sunday, March 20, 2011
Convexity - Some Facts
Convexity- Assets
Financial instruments that gains one unit and loses one unit for every step up and down respectively are called linear instruments. These instruments will gain or lose same amount in magnitude in rising and falling market. An example of this kind of instrument is Futures contract. There are instruments that increase or decrease in value at different magnitudes for different level of changes in markets. This class of instruments is termed as convex products. In this article I will discuss, some ways to synthesize convexity in 3m Libor interest rates, Swap rates and also Volatility.
Convexity in 3M Libor interest rates can be traded using Futures vs Forwards and 3m Libor interest rate swaps vs 3m Libor arrear swaps products. These two products provide a way to buy and sell convexity implied by the markets. Normally, in interest rate markets we see forward rates implied by 3M euro dollar interest rate future contracts are adjusted for convexity. This practice arises due to differences in settlement conventions for futures and forward contracts. More intuitively, future contracts settle daily and forwards settle once on the rate resetting date. This nuance looks very trivial but in some instances this can translate into huge amounts. Due to daily settlement feature in futures, investor in long futures contract has to maintain maintenance margin that needs to replenish as market falls and withdraw excess funds over this margin when market rises. Whereas, the investor in the over the counter forwards market has to wait till settlement date to act. In nutshell, futures investor can realize the market changes daily and forwards investor has to wait till settlement date to realize the market changes. In financial markets, present valuing of the cash flows is a way to compare different products. In this way, futures cash flows are discounted daily and forwards are discounted at term rates. So when rates rise by 1 bp, futures contract gains $ 25 and rates rise by 10 bp, $ 250 change in value is realized. Similarly, the position will lose, $ 25 and $250 dollars respectively. In forwards market, gain and loses are different in magnitude. This is because, when rates rise, we discount the cash flows with higher rate so less value and in a falling rates market, we discount cash flows with lower rates and hence higher value. This is called convexity. This is mainly dependent on correlation between discount rate and 3m Libor rate, and their volatilities to measure. A pair contract, future and forward locks current market implied convexity and this can be bought and sold based on current Libor cap market volatilities. Now moving from future vs Forward convexity to Libor swaps that exhibit convexity.
Standard 3m Libor Interest rate swaps with reset advance and pay in arrears contract features allows to trade the level of interest rate yield curve. At the same time with a small tweak to reset feature from advance to arrears will create an arrear swap. This swap will present an investor to trade level of the swap rate along with a view on the speed at which forward rates change in current yield curve. These two products are convex products when measured against movement of yield curves. But Libor in arrears swaps since resets and pays in arrears has additional convexity that is absent in plain vanilla swap. Why convexity is coming into picture here? What is the benefit of this convexity? In today’s yield curve there is a forward curve structure. This structure once locked will define the value of the swap. In arrear swap since rates are reset in future on the same date of payment, it creates small mismatch between the term of the rate (3m Libor) observed in arrears and the payment time or date. In a regular swap, rate is observed in advance and allowed to accrue till payment date which happens to be its term. Where as in arrear swap this accrual doesn’t happen and this creates an opportunity to its holder. If rates rise, the payer has to higher rate but discounted with a higher rate (so lower value) and vice versa. Also, if investor thinks yield curve will realize embedded forward curve at slower pace wants to receive fixed rate (convexity adjusted). This gives additional yield pickup. This convexity is measured using interest rate cap volatilities.
Now let us move to CMS convexity products. This class of products provides investors to take view on the CMS rates where investor pays or receives CMS rate vs 3M Libor + spread. This spread is normally quoted in the broker market as spread over Libor. Now convexity is lurking behind CMS rates in this product also. Answer to this would be, due to mismatch between CMS rate being observed and accrued. For instance, CMS 10y rate is observed for 3m and paid at the end of period. This mismatch between accrual period and observed rates gives rise to convexity. Now how do I measure this? This is measured by looking into swaption volatility market. CMS swap can be replicated by series out of the money puts and calls. In normal put call parity frame work, Cap-floor is equal to swap. So if we can price a series of these caps and floors accurately we can measure the convexity effectively.
Financial instruments that gains one unit and loses one unit for every step up and down respectively are called linear instruments. These instruments will gain or lose same amount in magnitude in rising and falling market. An example of this kind of instrument is Futures contract. There are instruments that increase or decrease in value at different magnitudes for different level of changes in markets. This class of instruments is termed as convex products. In this article I will discuss, some ways to synthesize convexity in 3m Libor interest rates, Swap rates and also Volatility.
Convexity in 3M Libor interest rates can be traded using Futures vs Forwards and 3m Libor interest rate swaps vs 3m Libor arrear swaps products. These two products provide a way to buy and sell convexity implied by the markets. Normally, in interest rate markets we see forward rates implied by 3M euro dollar interest rate future contracts are adjusted for convexity. This practice arises due to differences in settlement conventions for futures and forward contracts. More intuitively, future contracts settle daily and forwards settle once on the rate resetting date. This nuance looks very trivial but in some instances this can translate into huge amounts. Due to daily settlement feature in futures, investor in long futures contract has to maintain maintenance margin that needs to replenish as market falls and withdraw excess funds over this margin when market rises. Whereas, the investor in the over the counter forwards market has to wait till settlement date to act. In nutshell, futures investor can realize the market changes daily and forwards investor has to wait till settlement date to realize the market changes. In financial markets, present valuing of the cash flows is a way to compare different products. In this way, futures cash flows are discounted daily and forwards are discounted at term rates. So when rates rise by 1 bp, futures contract gains $ 25 and rates rise by 10 bp, $ 250 change in value is realized. Similarly, the position will lose, $ 25 and $250 dollars respectively. In forwards market, gain and loses are different in magnitude. This is because, when rates rise, we discount the cash flows with higher rate so less value and in a falling rates market, we discount cash flows with lower rates and hence higher value. This is called convexity. This is mainly dependent on correlation between discount rate and 3m Libor rate, and their volatilities to measure. A pair contract, future and forward locks current market implied convexity and this can be bought and sold based on current Libor cap market volatilities. Now moving from future vs Forward convexity to Libor swaps that exhibit convexity.
Standard 3m Libor Interest rate swaps with reset advance and pay in arrears contract features allows to trade the level of interest rate yield curve. At the same time with a small tweak to reset feature from advance to arrears will create an arrear swap. This swap will present an investor to trade level of the swap rate along with a view on the speed at which forward rates change in current yield curve. These two products are convex products when measured against movement of yield curves. But Libor in arrears swaps since resets and pays in arrears has additional convexity that is absent in plain vanilla swap. Why convexity is coming into picture here? What is the benefit of this convexity? In today’s yield curve there is a forward curve structure. This structure once locked will define the value of the swap. In arrear swap since rates are reset in future on the same date of payment, it creates small mismatch between the term of the rate (3m Libor) observed in arrears and the payment time or date. In a regular swap, rate is observed in advance and allowed to accrue till payment date which happens to be its term. Where as in arrear swap this accrual doesn’t happen and this creates an opportunity to its holder. If rates rise, the payer has to higher rate but discounted with a higher rate (so lower value) and vice versa. Also, if investor thinks yield curve will realize embedded forward curve at slower pace wants to receive fixed rate (convexity adjusted). This gives additional yield pickup. This convexity is measured using interest rate cap volatilities.
Now let us move to CMS convexity products. This class of products provides investors to take view on the CMS rates where investor pays or receives CMS rate vs 3M Libor + spread. This spread is normally quoted in the broker market as spread over Libor. Now convexity is lurking behind CMS rates in this product also. Answer to this would be, due to mismatch between CMS rate being observed and accrued. For instance, CMS 10y rate is observed for 3m and paid at the end of period. This mismatch between accrual period and observed rates gives rise to convexity. Now how do I measure this? This is measured by looking into swaption volatility market. CMS swap can be replicated by series out of the money puts and calls. In normal put call parity frame work, Cap-floor is equal to swap. So if we can price a series of these caps and floors accurately we can measure the convexity effectively.
Sunday, March 13, 2011
SABR Model overview
Breif presentation on SABR model and its applications to Interest Rates Swaption Market
Saturday, March 12, 2011
CMS spread options and Digitals - Market Nuances
CMS spread otions and Digitals (General facts)
ECB has raised the amber flag with regards to fighting inflation arising due to persistent higher oil prices. US FED is on permanent hold with regards to hiking interest rates. This is creating a divergence in front end of the yield curve. On the long end, 10y and 30y rates are currently gaining traction from anticipation of end of QE2 world in June 2011.
In Interest rate derivative markets, Options on Yield curve Spread and also digitals are traded very often. To provide Yield curve pick up to investors, often issuers come up with structured notes paying coupons tied to the Yield curve spreads. The Embedded options in these structured notes needs to be hedged by the dealers in the market. The Yield curve spread options can be created as spread between 30y and 2y rates above 0. This means Yield curve will not invert. Another class of notes will pay a coupon if this spread is above zero. This product is classified as spread digital product. In this article I would like discuss some market facts about Spread options and spread digital options.
Spread products: Primary driver for spread products is to make a bet on the shape of the yield curve and underlying correlation structure. Yield curves take variety of shapes, including flat, steep, inverted, concave, convex etc based on where the interest rates are trading in spot and forward space. Interesting aspect of the spread products is they capture the forward yield curve in the structure. For instance a spread option that pays when spread between 30y and 2y is above 0 every quarter 5y from today to 10y from today is betting on the yield curve in 5y forward. The market price of this option has a view on correlation between 30y and 2y rates. In this case, if an investor takes a position in a CMS spread option straddle, his core view is not on change in the shape of yield curve but change in the correlation. This means, he will buy the option if the yield curve is highly correlated and hence lower cost to get this option and at the same time he expects the correlation to fall. In other words, investor will be looking at higher implied correlations and fading them as time passes. This scenario can happen when yield curve steepening and flattening is accompanied by rising of 30y and falling of 2y and vice versa.
Now, let us take a look at actual markets.
Spot 2y rates is trading at 0.88 and spot 30y trading at 4.266. Similarly, 5y forward 2y is at 4.78 and 5y forward 30y is at 4.95. This clearly indicates, spot spread is at 338 and forward spread is flat 20bps. Just take a step back and understand the economic backdrop. USD fed has set the fed funds rates at very low (0 to 0.25 bps) and 2y rates are pegged to this fact. 30y rates are driven by growth in economy and inflation. As of today there is high uncertainty around these factors due to Fed Qe2 policy, Fiscal tug of war between US polity and economic recovery. Therefore, correlations have been on the rise due to this crisis phenomena. This suggests the Spread trades should be very cheap. There is a graph below that shows historical realized correlation between 5y forward 2y and 30y rates. I see current correlation is at 70%. But when I look at spread option market for quotes, I see market is very rich and it thinks implied correlations are very low. One answer to this is due to demand and supply in the market. That is there is huge bid for the CMS spread options and this is driving up the prices.
Now as I mentioned above CMS spread digitals are another class of products coming into existence due to hedging Range accrual products and opportunistic trades. Digital products trade prices are affected by two sources, one being steepness of yield curve and second being the underlying skew structure. Digitals can be valued as call spread or put spread options. In the case of a floor struck at 0, we will be modeling a bear put spread. In this we are long 0 strike put and short lower strike put. If low strike skew is rich and curve is steep we will see cheap digitals. Here also another interesting fact pattern arises that is when market has sold enough of these digitals due to low price and it being never getting into money and people are able to collect hefty premiums. At these low levels, people interested in buying tail hedges emerge to bid up the prices. This fascinating fact pattern attracts make me think how market players signal their one person’s rational behavior as other persons irrational behavior.
ECB has raised the amber flag with regards to fighting inflation arising due to persistent higher oil prices. US FED is on permanent hold with regards to hiking interest rates. This is creating a divergence in front end of the yield curve. On the long end, 10y and 30y rates are currently gaining traction from anticipation of end of QE2 world in June 2011.
In Interest rate derivative markets, Options on Yield curve Spread and also digitals are traded very often. To provide Yield curve pick up to investors, often issuers come up with structured notes paying coupons tied to the Yield curve spreads. The Embedded options in these structured notes needs to be hedged by the dealers in the market. The Yield curve spread options can be created as spread between 30y and 2y rates above 0. This means Yield curve will not invert. Another class of notes will pay a coupon if this spread is above zero. This product is classified as spread digital product. In this article I would like discuss some market facts about Spread options and spread digital options.
Spread products: Primary driver for spread products is to make a bet on the shape of the yield curve and underlying correlation structure. Yield curves take variety of shapes, including flat, steep, inverted, concave, convex etc based on where the interest rates are trading in spot and forward space. Interesting aspect of the spread products is they capture the forward yield curve in the structure. For instance a spread option that pays when spread between 30y and 2y is above 0 every quarter 5y from today to 10y from today is betting on the yield curve in 5y forward. The market price of this option has a view on correlation between 30y and 2y rates. In this case, if an investor takes a position in a CMS spread option straddle, his core view is not on change in the shape of yield curve but change in the correlation. This means, he will buy the option if the yield curve is highly correlated and hence lower cost to get this option and at the same time he expects the correlation to fall. In other words, investor will be looking at higher implied correlations and fading them as time passes. This scenario can happen when yield curve steepening and flattening is accompanied by rising of 30y and falling of 2y and vice versa.
Now, let us take a look at actual markets.
Spot 2y rates is trading at 0.88 and spot 30y trading at 4.266. Similarly, 5y forward 2y is at 4.78 and 5y forward 30y is at 4.95. This clearly indicates, spot spread is at 338 and forward spread is flat 20bps. Just take a step back and understand the economic backdrop. USD fed has set the fed funds rates at very low (0 to 0.25 bps) and 2y rates are pegged to this fact. 30y rates are driven by growth in economy and inflation. As of today there is high uncertainty around these factors due to Fed Qe2 policy, Fiscal tug of war between US polity and economic recovery. Therefore, correlations have been on the rise due to this crisis phenomena. This suggests the Spread trades should be very cheap. There is a graph below that shows historical realized correlation between 5y forward 2y and 30y rates. I see current correlation is at 70%. But when I look at spread option market for quotes, I see market is very rich and it thinks implied correlations are very low. One answer to this is due to demand and supply in the market. That is there is huge bid for the CMS spread options and this is driving up the prices.
Now as I mentioned above CMS spread digitals are another class of products coming into existence due to hedging Range accrual products and opportunistic trades. Digital products trade prices are affected by two sources, one being steepness of yield curve and second being the underlying skew structure. Digitals can be valued as call spread or put spread options. In the case of a floor struck at 0, we will be modeling a bear put spread. In this we are long 0 strike put and short lower strike put. If low strike skew is rich and curve is steep we will see cheap digitals. Here also another interesting fact pattern arises that is when market has sold enough of these digitals due to low price and it being never getting into money and people are able to collect hefty premiums. At these low levels, people interested in buying tail hedges emerge to bid up the prices. This fascinating fact pattern attracts make me think how market players signal their one person’s rational behavior as other persons irrational behavior.
Thursday, March 10, 2011
Swaption Skew at Febraury 28 2011
Libor Swap Market Skew takes different shapes as of February month end. The profile of this skew for Receivers vs payers looks as shown in above table.
I have classified the skew to be Lognormal ( volatility rises proportianl to rates) and Norma (Rates are independent of volatilities). If the dynamics are some where in between then i will call it as Quarter power and square root.
For more detail looks for my previous postings on this topic
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