Doctoral thesis: New option pricing models with more efficient estimation of implied volatility

Doctoral thesis: New option pricing models with more efficient estimation of implied volatility

Financial modelling is the art of searching for the best quantitative solution to the problem. Since the stock market crash of October 1987, modelling implied volatility increasingly became a non-trivial issue.

The approach for computing implied volatility turned out to be considerably more complex than the pricing formula itself. In her doctoral thesis Kun Huang investigates and develops efficient option pricing models which can be used in equity and interest rate derivative markets. The approaches introduced in her thesis produce arbitrage-free implied volatility.

- There is no universal model in derivative markets. Practically, different option pricing models are used in different derivative markets. My thesis investigates option pricing models used in foreign exchange option, equity option and interest rate option markets, says Huang.

Huang is the first to explore the efficiency of the Vanna Volga method, for pricing S&P 500 index options. The Vanna Volga method is widely used in foreign exchange option market, but doesn’t attract attention in other derivative markets.  The compelling results show its good performance for pricing equity index options.

-A well-behaved model for explaining volatility smile should consider the local, stochastic and jump features of volatility dynamics, and mix them in the right proportion, says Huang.

In her thesis Huang also develops a hybrid model which combines the advantages of the stochastic volatility and local volatility models. The hybrid model yields particularly good results when the stochastic process of underlying asset price and its variance are simulated using a quasi-Monte Carlo method with Romberg extrapolation in the case of an independent Brownian motion.

-Hagan’s asymptotic formula for implied volatility, which is built under the SABR process, has been the benchmark for pricing and hedging interest rate derivatives. Its weakness came to light in the case of low and negative interest rate, which is a feature of financial market now.

The breakdown of Hagan’s formula can be ascribed to several issues related to the probability mass of the forward rate being zero. The new asymptotic formula studied in Huang’s thesis can cope with the low and negative interest rate issue. Her formula is built under the SABR process and takes into account the probability mass of the forward rate being zero, says Huang.

You can read the doctoral thesis here.

Kun Huang will defend her doctoral thesis in Finance and Statistics entitled ‘Implied Volatility and Option Pricing Models’ on Friday 8 February 2019 at noon.

Place: Hanken School of Economics, Kirjastonkatu 16, Vaasa
Opponent and university: Professor Seppo Pynnönen, University of Vaasa
Custos: Kenneth Högholm

More information:
Kun Huang
Mobile: +358 469 371 493