Synopsis for Financial Derivatives 2

Further details (Dr Hanqing Jin - 16 lectures - HT - Core Course)
This course builds on Financial Derivatives 1. We continue the analysis of derivatives pricing and hedging within the Black-Scholes modelling framework but look at more complex (exotic and American) contracts. We then review assumptions of the Black-Scholes model, discuss its drawbacks and weaknesses and generalise our analysis to more involved market modelsSynopsisFundamentals: self-financing portfolios and pricing via hedging, Fundamental Theorems of Asset Pricing in continuous times;Simple exotic options: forward strat, compound options; Exotic options,Barrier, Lookback and Asian options; American options: PDE vs Stochastic approach; Black-Scholes defaults and model-free pricing and hedging;Local and Stochastic Volatility models;

The course will be mainly based on

• S Shreve, Stochastic Calculus for Finance II (Continuous-Time Models), Springer (2004)
  with frequent excursions to
  
• M Musiela and M Rutkowski, Martingale Methods in Financial Modelling, 2nd Ed, Springer (2005)
• P Wilmott, S D Howison and J Dewynne, Mathematics of Financial Derivatives, CUP (1995) for arguments from martinagle theory and PDEs respectively.
  
  Other helpful references include:
• T Bjork, Arbitrage Theory in Continuous Time, OUP (1998)
• A Etheridge, A course in Financial Calculus, CUP (2002)
• J Gatheral, The Volatility Surface: A Practicioner's Guide, Wiley (2006) Additional notes may be distributed during the course.