TY: THES
T1 - Three essays on option pricing
A1 - Cruz, Aricson César Jesus da
N2 - This thesis addresses option pricing problem in three separate and self-contained papers:
A. The Binomial CEV Model and the Greeks
This article compares alternative binomial approximation schemes for computing the option hedge ratios studied by Pelsser and Vorst (1994), Chung and Shackleton (2002), and Chung et al. (2011) under the lognormal assumption, but now considering the constant elasticity of variance (CEV) process proposed by Cox (1975) and using the continuous-time analytical Greeks recently offered by Larguinho et al. (2013) as the benchmarks. Among all the binomial models considered in this study, we conclude that an extended tree binomial CEV model with the smooth and monotonic convergence property is the most efficient method for computing Greeks under the CEV diffusion process because one can apply the two-point extrapolation formula suggested by Chung et al. (2011).
B. Valuing American-Style Options under the CEV Model: An Integral Representation Based Method
This article derives a new integral representation of the early exercise boundary for valuing American-style options under the constant elasticity of variance (CEV) model. An important feature of this novel early exercise boundary characterization is that it does not involve the usual (time) recursive procedure that is commonly employed in the so-called integral representation approach well known in the literature. Our non-time recursive pricing method is shown to be analytically tractable under the local volatility CEV process and the numerical experiments demonstrate its robustness and accuracy.
C. A Note on Options and Bubbles under the CEV Model: Implications for Pricing and Hedging
The discounted price process under the constant elasticity of variance (CEV) model is not a martingale for options markets with upward sloping implied volatility smiles.
The loss of the martingale property implies the existence of (at least) two option prices for the call option, that is the price for which the put-call parity holds and the price representing the lowest cost of replicating the payoff of the call. This article derives closed-form solutions for the Greeks of the risk-neutral call option pricing solution that are valid for any CEV process exhibiting forward skew volatility smile patterns. Using an extensive numerical analysis, we conclude that the differences between the call prices and Greeks of both solutions are substantial, which might yield significant errors of analysis for pricing and hedging purposes.
UR - https://repositorio.iscte-iul.pt/handle/10071/18898
Y1 - 2019
PB - No publisher defined