1 - 7 of 7 Chapters
[This book is about a study on the calculation of option Greeks using discrete Malliavin calculus. Greeks are quantities that represent the price sensitivities of derivative securities with respect to changes in the underlying asset price or parameters.]
[In this chapter, we present a one-period security price valuation model. Although this is a very straightforward model, it already contains the structure of Malliavin calculus.]
[In this chapter, we introduce discrete-time stochastic processes. We show that we can consider Ito formulas even in discrete-time models, which are very useful in continuous-time stochastic processes.]
[The pricing of options using the tree approach is discussed in this chapter. In a binomial tree approach, it is usual to calculate the price backward. We briefly discuss some other methods, usage of the Fourier transform approach. We also would like to briefly mention the computation method of...
[This chapter introduces new and significantly fast algorithms to evaluate the price of double barrier options using binomial trees. To compute the price of double barrier options accurately, trees with large numbers of steps must be used, which is time-consuming. In order to overcome this...
[In this chapter, we give a brief explanation of a continuous-time setting. The idea of this this chapter originates from the work by Montero and Kohatsu-Higa (2003).]
[This chapter provides new methods for computation of Greeks using the binomial tree and the discrete Malliavin calculus. In the last decade, the Malliavin calculus has come to be considered as one of the main tools in financial mathematics. It is particularly important in the computation of...
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