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Computational Methods for Pricing and Hedging Derivatives

Paletta, Tommaso (2015) Computational Methods for Pricing and Hedging Derivatives. Doctor of Philosophy (PhD) thesis, University of Kent,.

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Abstract

In this thesis, we propose three new computational methods to price financial derivatives and construct hedging strategies under several underlying asset price dynamics. First, we introduce a method to price and hedge European basket options under two displaced processes with jumps, which are capable of accommodating negative skewness and excess kurtosis. The new approach uses Hermite polynomial expansion of a standard normal variable to match the first m moments of the standardised basket return. It consists of Black-and-Scholes type formulae and its improvement on the existing methods is twofold: we consider more realistic asset price dynamics and we allow more flexible specifications for the basket. Additionally, we propose two methods for pricing and hedging American options: one quasi-analytic and one numerical method. The first approach aims to increase the accuracy of almost any existing quasi-analytic method for American options under the geometric Brownian motion dynamics. The new method relies on an approximation of the optimal exercise price near the beginning of the contract combined with existing pricing approaches. An extensive scenario-based study shows that the new method improves the existing pricing and hedging formulae, for various maturity ranges, and, in particular, for long-maturity options where the existing methods perform worst. The second method combines Monte Carlo simulation with weighted least squares regressions to estimate the continuation value of American-style derivatives, in a similar framework to the one of the least squares Monte Carlo method proposed by Longstaff and Schwartz. We justify the introduction of the weighted least squares regressions by numerically and theoretically demonstrating that the regression estimators in the least squares Monte Carlo method are not the best linear unbiased estimators (BLUE) since there is evidence of heteroscedasticity in the regression errors. We find that the new method considerably reduces the upward bias in pricing that affects the least squares Monte Carlo algorithm. Finally, the superiority of our new two approaches for American options are also illustrated over real financial data by considering S&P 100 options and LEAPS®, traded from 15 February 2012 to 10 December 2014.

Item Type: Thesis (Doctor of Philosophy (PhD))
Thesis advisor: Tunaru, Radu
Thesis advisor: Stanescu, Silvia
Uncontrolled keywords: Quantitative Finance, Basket options, Spread options, American options, Monte Carlo methods, Quasi-analytic methods, Moment-matching, Extension method, Weighted least squares
Subjects: H Social Sciences > HF Commerce > HF5351 Business
H Social Sciences > HG Finance
Divisions: Faculties > Social Sciences > Kent Business School
Depositing User: Users 1 not found.
Date Deposited: 29 Jun 2015 17:00 UTC
Last Modified: 29 May 2019 14:45 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/49180 (The current URI for this page, for reference purposes)
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