Computational methods for pricing and hedging derivatives

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