Probabilistic methods in exotic option pricing

The thesis presents three ways of calculating the Parisian option price as an illustration of probabilistic methods in exotic option pricing. Moreover options on commidities are considered and double-sided barrier options in a compound Poisson framework.Electrical Engineering, Mathematics and Computer Scienc

Indonesian options

Jakarta Stock Exchange Indonesia has started to trade Indonesian options at September 9th, 2004. An Indonesian option can be considered as an American style barrier option with immediate (forced) exercise if the price hits or crosses the barrier before maturity. The payoff of the option is based on a moving average of the price of the underlying stock. The barrier is fixed at the strike price plus or minus a 10 percent. The option is automatically exercised when the underlying stock hits or crosses the barrier and the difference between strike and barrier is paid immediately. We will refer to type of this option as Indonesian option. In this paper we study the pricing of the Indonesian option in a Black-Scholes economy. We will derive analytic approximations for the option price. We will discuss volatility and it turns out that expression we cannot calculate the implied volatilities.Electrical Engineering, Mathematics and Computer Scienc

A Benchmark Approach of Counterparty Credit Exposure of Bermudan Option under Lévy Process: The Monte Carlo-COS Method

An advanced method, which we call Monte Carlo-COS method, is proposed for computing the counterparty credit exposure profile of Bermudan options under Lévy process. The different exposure profiles and exercise intensity under different mea- sures, P and Q, are discussed. Since the COS method [1] delivers accurate Bermudan prices, and no change of measure [2] needed to get the P-probability distribution, the exposure profile produced by the Monte Carlo-COS algorithm can be used as a benchmark result, E.g., to analyse the reliability of the popular American Monte Carlo method [3], [4] and [5]. The efficient calculation of expected exposure (EE) [6] can be further applied to the computation of credit value adjustment (CVA) [6].Delft Institute of Applied MathematicsElectrical Engineering, Mathematics and Computer Scienc