### CSCI 381.3/780 - COMPUTATIONAL FINANCE

Valuation of financial derivatives as a family of algorithmic
computations. Analysis of interactions between the underlying financial
models (assumptions and constructions) and the efficiency (time and
resources) of implementation of these algorithms. Hands-on
implementation practice. Topics include concept of a derivative
contract and the problem of its pricing; time value of money; market
risk and the concept of risk-free portfolio; arbitrage as a valuation
axiom; valuation of forward and futures contracts on stock, currencies,
interest-rates, indices, commodities; collateral, marking-to-market,
margining, and netting; fundamentals of capital asset pricing model and
correlations as a valuation assumption; translations among yield curves,
bond prices and forward interest rates; valuation of swaps
(interest-rate and currency); arbitrage-based valuation of options,
option contract as a basic non-linear element in claim construction;
binomial trees for option pricing, and the concept of risk-free
valuation and recursion from the final claim value; modeling stochastic
behavior with Weiner processes, ItÃ´ Lemma, the Black-Scholes-Merton
model for options; Greeks; volatility smiles and the concept of
market-implied computational context; credit risk, estimates of default
probabilities from prices of corporate bonds and equity, translations
between credit default spreads and default intensities; introduction to
issues in valuation of some path dependent and exotic derivatives.

Textbook: Options, Futures, and Other Derivatives by J. C. Hull.