Monte Carlo Based Numerical Pricing of Multiple Strike-Reset Options - Christodoulou, S (oxford university;mathematical institute, 2011)
In the last few years the complexity of some contracts offered by many financial markets has increased a lot. A common but complex financial contract is the Shout option, which grants the allowance to the holder to alter certain features of this contract, according to some specific rules. An example of a Shout option, and the one analysed in this thesis, is the Strike Reset option, which grands the option holder the right to reset the strike of the option a predetermined number of times before maturity. The pricing and hedging of these contacts is much more complex than the simple European options, and for most of them there does not exist a closed form formulae. As a result the valuation of these options is mainly done using multiple layer binomial trees, using Finite Difference methods or using Monte-Carlo techniques. [6] and [5] analyse the Strike Reset Put option on a single underlying asset and consider optimal reset policies using a PDE approach. Moreover [19] uses Finite Difference methods to price Strike Reset Put options with more complex restrictions in the reset features. In this thesis we use Least Squares Regression method, which was introduced by Longstaff and Schwartz, to price the Strike Reset Put option. Moreover we use Pathwise Sensitivities Approach and Likelihood Ratio Method to obtain the Greeks of this Strike Reset option within the Monte Carlo framework. Note that this thesis is an extension of a previous thesis, [20], submitted by Yudaken, where in this thesis we handle the increased complexity due to the multiple strike resets that the holder of the option has. Note that we present all theoretical and numerical results for the specic case of Strike Reset Put option. These results can be very easily extended to similar Strike Reset options, for example the Strike Reset Call option and the Strike Reset Asian Call and Put options. This thesis is structured as follows. In chapter 1, we present a description of the Strike Reset option. Then we extend the Least Squares approach to price the Strike Reset Put option. Moreover we present theoretical results for estimating the sensitivities of this option using Likelihood Ratio Method and Pathwise Sensitivities Approach. In chapter 2, we present numerical results for modelling the Strike Reset Put option. This thesis ends by a conclusion and a suggestion for possible extensions.