De Simone, Antonio
(2013)
A Two-Factor Binomial Model for Pricing Hybrid Securities: A Simplified Approach.
[Tesi di dottorato]
Abstract
This thesis develops a numerical procedure for pricing financial contracts whose contingent claims are exposed to two sources of risk: the stock price and the short interest rate. Particular emphasis here is placed on hybrid financial securities, i.e. on a group of financial contracts that combine the elements of the two broader groups of securities, debt and equity. Moreover, we focus on "American style" financial products, i.e. financial contracts (such as American options or convertible bonds) giving the owner a right to be exercised within a certain date. In particular, the proposed pricing framework assumes that the stock price dynamics is described by the Cox, Ross Rubinstein (CRR, 1979) binomial model under a stochastic risk free rate, whose dynamics evolves over time accordingly to the Black, Derman and Toy (BDT, 1990) one-factor model. We also show how to apply the numerical procedure to compute the price of three financial contracts with increasing complexity: a vanilla (European and American) call option, a callable convertible bond and a participating policy, i.e. an insurance contract where the benefit for the policyholder is partly fixed and partly variable, depending on the profit of the insurance company. We also discuss some issues related to the implementation and calibration of such a two factors numerical procedure and in particular how the dynamics of each risk factor can calibrated to the observed market prices. Finally, in order to assess the validity of the model, its advatages and drawbacks, we conduct an empirical analysis where, in particular, the role of the correlation between stock price and interest rate is emphasized. We study different possible ways for calibrating the correlation parameter, including implied correlation and multivariate GARCH forecast.
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