Credit Spread Options And Its Valuation With Monte Carlo Simulations

Option is a financial derivatives generated in mid-1970s in the United States , it has beenwidely used in hedging, risk management and prices speculation. Option contracts give the holdera right rather than an obligation. From the 1980s debt crisis, the concentrations on the bank'scredit risk have become a tricky problem. Some of the large financial institutions are usually ina dilemma situation that leads to worry about the excessive concentrations on the credits of somecountries or golbal corporations for one aspect, and to fear of losing customers and business butcontinuing to do business for other aspect. Credit derivative products resolve partially this problemwhich makes the financial institutions both continuing to kept in touch with their customer andremoving the credit risk concentration with credit derivatives. Pricing credit spread Options hasbecome a main topic in the field of option pricing, and is also an option whose underlying is thecredit spreads. With paying the option fee to the short position, the Long position of the creditspread option can get the rights which the liquidity requirements for the implementation of optionsshort of the rights that the option holder if the market access in the future yield spreads higher thanthe prior agreement, i.e., the holder (also called the protector of the long position) can transfer thevolatility risks of the market credit spread by paying some option fees. The so-called credit spreadis defined as a yield difference between the sensitive bonds (such as high-risk high-yield bonds)and the risk-free bonds (Treasuries). This paper considers mainly the pricing problem on somepath-dependent credit spread options under the LS model by using the measure change technique,martingale method and the multidimensional normal distribution, our main conclusions includeas follows,Chapter I introduces some literature reviews on the pricing of the credit spread option, Se-lected topic base and related existent results.In Chapter II, the pricing problems of both the fixed Asian credit spread option and the ?oatingAsian credit spread option are discussed. We derive firstly the closed-form solution of the pricefor the geometric-average option which is used as a control variable to simulate the approximationof the arithmetic-average option. Secondly, we apply the reduced variance technique to simulatethe price of the arithmetic-average Asian credit spread option. Finally, some numerical examples are provided to analyze the option prices of different credit grade and effects of the volatility ofthe credit spread on option prices.In Chapter III, the valuation of an European-style credit spread reset option is considered.With the similar arguments in Chapter II, the prices of both the credit spread reset option withsingle reset date and the Asian-style credit spread reset option with single reset date are obtained.The comparisons between the vanilla credit spread option and the credit spread reset options aremade with numerical experiments. It is found that the credit spread reset options has the similarfeatures to the stock options.In Chapter IV, we discuss mainly the pricing of an American-style credit spread option. It iswell known that American options can only be evaluated numerically with few exceptions. Theaim of this chapter is to present three alternative approaches for valuing American options writtenon credit spreads. These approaches include the compound option approach, the Least SquaresMonte Carlo approach(LSM), and the Perfect Foresight Monte Carlo approach(PFM) which havebeen applied successfully to value American options written on stocks. The numerical implemen-tation shows that the PFM is more suitable for simulated pricing the credit spread options than theLSM.