Master of Science (MSc)
Faculty of Science
Giuseppe (Joe) Campolieti
By employing a randomization procedure on the geometric Brownian motion (GBM) model, we construct our new pricing models with stochastic volatility exhibiting symmetric smiles in the log-forward moneyness, and admitting simple closed-form analytical expressions for European-style option prices. We assume that there are no infinitesimal correlations between the underlying asset prices and their volatility, and the integrated squared volatility processes are random variables with well-known probability density functions. Under some regularity conditions, closed-form expressions are obtained by taking the expectation of option prices under diffusion models over the integrated squared volatility process, which relate to the Bayesian framework in the GBM model studied by Darsinos and Satchell . Surprisingly, the pricing formulas for the novel models presented in this thesis are even simpler than the classical GBM model as they are expressed as elementary analytical functions. The option prices are also obtained numerically in an efficient manner since they only involve one-dimensional integrals of complementary error functions with respect to the variable of integration. We also calibrate to the market data from Coca Cola to compare the performance on the new models and the SABR model.
Kato, Hiromichi, "Asset Pricing under Randomized Solvable Diffusions" (2020). Theses and Dissertations (Comprehensive). 2329.