Quanto Credit Hedging

Quanto Credit Hedging
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Published Date:26-07-2017
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Lecture 23 Quanto Credit Hedging Dr. Stefan Andreev (Executive Director, Morgan Stanley) Developed for educational use at MIT and for publication through MIT OpenCourseware. No investment decisions should be made in reliance on this material. Guide Stefan Andreev Stefan Andreev is the head strat for Fixed Income Emerging Markets in Europe and Americas, as well as the head strat for Fixed Income Structured Bonds. Mr. Andreev joined the Firm in January 2006 as an Emerging Markets strat. Prior to that, Mr. Andreev completed a Ph.D. in Chemical Physics at Harvard University. Mr. Andreev has a Bachelor’s degree from Dartmouth College. Mr. Andreev’s comments today are his own, and do not necessarily represent the views of Morgan Stanley or its affiliates, and are not a product of Morgan Stanley Research. 2 2 Developed for educational use at MIT and for publication through MIT OpenCourseware. No investment decisions should be made in reliance on this material.Big Picture Pricing/Hedging  Topic: Pricing/Hedging  Basic concepts  Main focus: FX  Interest Rates  Credit  Mathematical Techniques  Risk-neutral pricing through expectations Stats/Predictions  Jump processes  Financial applications  Sovereign defaults and currencies (PIIGS and EUR)  Quanto Credit Developed for educational use at MIT and for publication through MIT OpenCourseware. 3 No investment decisions should be made in reliance on this material. FX – Foreign Exchange  Spot FX (USD/EUR)– Current exchange rate in USD for 1 EUR  Alternatively, the price in USD of 1 EUR  Denote spot FX rate by S. S is often modeled as a stochastic process, a Brownian motion with drift 4 Developed for educational use at MIT and for publication through MIT OpenCourseware. No investment decisions should be made in reliance on this material.Guide 4.69 FX forwards and interest rate parity  Forward FX contract is an agreement to exchange X EUR for Y USD at time T in the fd rrTt FSe future. Y/X is the Forward Rate tTt  The fair forward FX rate is determined by interest rates and spot FX  Continuous interest rates: 5 Developed for educational use at MIT and for publication through MIT OpenCourseware. No investment decisions should be made in reliance on this material.Guide 4.69 Interest Rates and compound interest  Risk free instantaneous interest rate r  Useful modeling approximation, does not quite exist in reality  Investing money B at time 0 earns a risk free return so that at time T in the future you have Bexp(rT)  Each currency has its own interest rates dS fd t rr dt dW t S t  Same as Black Scholes, solving the SDE we get fd 2 rr / 2dtW t SSe t 0 fd rrdt ES Se t 0  In this model, we can price various FX derivatives, such as FX forwards or options 6 Developed for educational use at MIT and for publication through MIT OpenCourseware. No investment decisions should be made in reliance on this material.Guide 4.69 FX Betting Game  Assumptions Pop Quiz Which game is  USD/EUR Spot is 1 better?  USD/EUR FX forward in 1 month is 1 A. Payoff A  Bet B B. Payoff B  If USD/EUR is more than 1 in 1 month, you lose C. Both are equal  If USD/EUR is less than 1 in 1 month, you win Outcome Payoff A h Payoff B h USD/EUR 1 -100 USD -100 EUR USD/EUR 1 +100 USD +100 EUR 7 Developed for educational use at MIT and for publication through MIT OpenCourseware. No investment decisions should be made in reliance on this material.Guide 4.69 FX Betting Game – Scenario Analysis  Run some scenarios and compare the payoff of each bet Scenario (in 1M) Bet A Bet B Bet A – Bet B USD/EUR = 1.25 -100 USD -100 EUR +25 USD = +19 EUR USD/EUR = 0.75 +100 USD +100 EUR +25 USD = +31 EUR 8 Developed for educational use at MIT and for publication through MIT OpenCourseware. No investment decisions should be made in reliance on this material.Guide 4.69 FX Betting Game – Scenario Analysis Guide 2.68 Subtitle Guide 2.64 Guide 1.95  Run some scenarios and compare the payoff of each bet Guide 1.64  Bet A is better each time, even though both payoffs are symmetric Scenario (in 1M) Bet A Bet B Bet A – Bet B Guide 0.22 USD/EUR = 1.25 -100 USD -100 EUR +25 USD = +19 EUR USD/EUR = 0.75 +100 USD +100 EUR +25 USD = +31 EUR Only Only Source / Source / Footnotes Footnotes below this below this line line Guide 2.80 9 Developed for educational use at MIT and for publication through MIT OpenCourseware. No investment decisions should be made in reliance on this material.Guide 4.69 FX Betting Game – Scenario Analysis  Run some scenarios and compare the payoff of each bet  Bet A is better each time, even though both payoffs are symmetric Scenario (in 1M) Bet A Bet B Bet A – Bet B USD/EUR = 1.25 -100 USD -100 EUR +25 USD = +19 EUR USD/EUR = 0.75 +100 USD +100 EUR +25 USD = +31 EUR  Lesson – the currency of the payoff matters when winning the bet is correlated with FX – the game is not symmetric anymore. 10 Developed for educational use at MIT and for publication through MIT OpenCourseware. No investment decisions should be made in reliance on this material.Guide 4.69 Reality Check: Italy Bonds  Italy issues bonds in both EUR and USD (among others), total 1.3 trillion of bonds  Cross-default: bonds of all currencies default together  Potential reasons to issue in USD  Access to other, potentially bigger pool of investors  Italy is an exporter, much revenue is in USD  Credit spread is the premium required for borrowing over the benchmark  Higher rates to borrow EUR than Germany  Higher rates to borrow USD than USA  Questions  Which currency does Italy prefer to raise money?  Which currency investors prefer? 11 Developed for educational use at MIT and for publication through MIT OpenCourseware. No investment decisions should be made in reliance on this material.Guide 4.69 Reality Check: Italy Bonds  Italy issues bonds in both EUR and USD (among others), total 1.3 trillion of bonds  Cross-default: bonds of all currencies default together  Potential reasons to issue in USD  Access to other, potentially bigger pool of investors  Italy is an exporter, much revenue is in USD  Credit spread is the premium required for borrowing over the benchmark  Higher rates to borrow EUR than Germany Pop Quiz  Higher rates to borrow USD than USA Italy pays higher credit spread premium in A. USD B. EUR C. Equal in both 12 Developed for educational use at MIT and for publication through MIT OpenCourseware. No investment decisions should be made in reliance on this material.Guide 4.69 Reality Check: Italy Bonds  Italy credit spread and EUR/USD FX rates are volatile  Pricing questions  How do you compare the value of EUR bonds vs. USD bonds?  How do you come up with a strategy to replicate USD bonds with EUR bonds?  Similarities to the FX betting game  Is value of the payoff currency correlated with the payoff event?  Theoretical pricing argument 1. Analyze the payoff of both instruments 2. Use math finance to price (replicating trading strategy) bonds 3. Obtain intuitive understanding (rules of thumb) from the results 13 Developed for educational use at MIT and for publication through MIT OpenCourseware. No investment decisions should be made in reliance on this material.Italy Credit Spreads: EUR vs. USD (adj. for basis) 600 Italy EUR 5Y bond spread Italy USD 5Y bond spread 500 400 300 200 100 - Date 14 Developed for educational use at MIT and for publication through MIT OpenCourseware. No investment decisions should be made in reliance on this material. 2-Apr-12 9-Apr-12 16-Apr-12 23-Apr-12 30-Apr-12 7-May-12 14-May-12 21-May-12 28-May-12 4-Jun-12 11-Jun-12 18-Jun-12 25-Jun-12 2-Jul-12 9-Jul-12 16-Jul-12 23-Jul-12 30-Jul-12 6-Aug-12 13-Aug-12 20-Aug-12 27-Aug-12 3-Sep-12 10-Sep-12 17-Sep-12 24-Sep-12 Credit Spread . Replication/Arbitrage strategy  Bonds regimes: performing and non-performing (default)  Complete market = replicating strategy exists  Goal is to replicate one bond with another in both regimes  Example:  Two zero-coupon bonds (E and U), same maturity, pay 100 at maturity T.  U pays 100 USD, E pays 100 EUR  Price of U=Pu; Price of E=Pe;  Spot FX=St; FX forward to T=Ft (USD/EUR)  Trivial potential arbitrage strategy of 1000 E bond with U bonds (initial price= 1000Pe)  Sell 1000Ft U bonds with proceeds 1000FtPu  Buy 1000 E bonds at cost 1000Pe  Enter into long USD FX forward (will be buying USD and selling EUR) for 100,000 EUR for maturity T at 0 cost 15 Developed for educational use at MIT and for publication through MIT OpenCourseware. No investment decisions should be made in reliance on this material.Potential Strategy: Payoff  Strategy Payoff: 100,000 EUR You Market EUR Bond 100,000 EUR FX Forward 100,000Ft USD 100,000Ft USD USD Bond  Net payoff: 0  Is the strategy an arbitrage if initial cost is not 0, i.e. if FtPu ≠SPe ? 16 Developed for educational use at MIT and for publication through MIT OpenCourseware. No investment decisions should be made in reliance on this material.Replication/Arbitrage strategy cont’d  Arbitrage: Start with 0 money, make money with non-zero probability  What happens if bond defaults?  Each bond pays the same % of notional, called recovery rate, typically much less than 100%  For sovereign issuers, expected recovery rate around 25%  Strategy payoff in case of default with 25% recovery rate:  Receive 25,000 EUR from bonds E  Convert 25,000 EUR to 25,000Ft USD using the FX forward ()  Pay 25,000Ft USD on short bond U position  Still left with 75,000 EUR FX forward  If EUR weakens strongly on default, you win big If it strengthens, you lose big  Strategy is NOT an arbitrage, not effective in replicating cashflows in all scenarios 17 Developed for educational use at MIT and for publication through MIT OpenCourseware. No investment decisions should be made in reliance on this material.Argentinean Peso/USD Devaluation on Credit Default Argentina Default December 30,2001 Guide 2.80 18 Developed for educational use at MIT and for publication through MIT OpenCourseware. No investment decisions should be made in reliance on this material.Applying mathematical finance  Can we do better? Need a model that captures essential features of the market  Mathematical model - hedging/replication strategy  Essential Model Features  Possibility of a credit event (default)  FX changes on default  Complete market  Number of hedging instruments ≥ number of model stochastic variables / sources  Pricing gives a replicating strategy, means that the price is unique  In practice, we try to model complete markets, even if some of the instruments do not actually trade 19 Developed for educational use at MIT and for publication through MIT OpenCourseware. No investment decisions should be made in reliance on this material.How do we use a model in trading? 1. Define the model with the desired dynamics  Check that the market in the model is complete  Check that it represents the salient features of the market 2. Price all the instruments  Generally, you need to solve a stochastic equation  Analytically  Numerically (PDE solvers, Monte Carlo simulations) 3. The sensitivity of the target instrument price to the prices of the replicating instruments gives you the hedging ratios (how much to buy or sell for the replicating portfolio)  Price(target) Hedge Ratio of instrument A  Price(hedge A) Guide 2.80 20 Developed for educational use at MIT and for publication through MIT OpenCourseware. No investment decisions should be made in reliance on this material.

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