This paper investigates the valuation of European option with credit risk in a reduced formmodel when the stock price is driven by the so-called Markov-modulated jump-diffusion process, in which the arrival rate of rare events and the volatility rate of stock are controlled by a continuous-time Markov chain. We also assume that the interest rate and the default intensity follow the Vasicek mode...

The option pricing problem is one of central contents in modern finance. In this paper, European option pricing formula is formulated for fuzzy financial market and some mathematical properties of them are discussed. This formula may be regarded as the fuzzy counterpart of Black-Scholes option pricing formula. In addition, some illustrative examples are also documented with MATLAB codes. c ©200...

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Following the economic rationale of [10] and [11] we present a new class of lookback options (by first studying the canonical ‘Russian’ variant) where the holder enjoys the early exercise feature of American options whereupon his payoff (deliverable immediately) is the ‘best prediction’ of the European payoff under the hypothesis that the true drift of the stock price equals a contract drift. I...

Option is derivative instrument that have investment benefit and provide return for the writer and the holder. Option price determination is affected by risk factor. However in Black-Scholes model option price is determined without arbitrage risk affection so it is impossible to take return. In this study, option price formula is constructed to be more represent the condition of financial marke...

A stochastic model for pure-jump diffusion (the compound renewal process) can be used as a zero-order approximation and as a phenomenological description of tick-by-tick price fluctuations. This leads to an exact and explicit general formula for the martingale price of a European call option. A complete derivation of this result is presented by means of elementary probabilistic tools. JEL G13

The problem of determining the European-style option price in the incomplete market has been examined within the framework of stochastic optimization. An analytic method based on the discrete dynamic programming equation (Bellman equation) has been developed that gives the general formalism for determining the option price and the optimal trading strategy (optimal control policy) that reduces t...

The problem of determining the European-style option price in the incomplete market has been examined within the framework of stochastic optimization. An analytic method based on the discrete dynamic programming equation (Bellman equation) has been developed that gives the general formalism for determining the option price and the optimal trading strategy (optimal control policy) that reduces t...

Following the economic rationale of [7] and [8] we present a new class of Asian options where the holder enjoys the early exercise feature of American options whereupon his payoff (deliverable immediately) is the ‘best prediction’ of the European payoff under the hypothesis that the true drift of the stock price equals a contract drift. Inherent in this is a protection feature which is key to t...

Keywords: Multiasset options Option sensitivities or Greeks Malliavin calculus Monte Carlo and quasi-Monte Carlo methods a b s t r a c t This paper discusses simulation of sensitivities or Greeks of multiasset European and Asian style options by Malliavin calculus combined with Monte Carlo and quasi-Monte Carlo methods. By using the Malliavin calculus, we are able to express Greeks of both Euro...