Applied Mathematics and Finance
(Leader: Prof. Yuncheng You )
Thursday, April 21, 2005
| Topic |
The Valuation Formulas for Compound Options |
| Speaker |
Elena Valkanova |
| Time |
11:00-12:00 p.m. |
| Place |
PHY 013 |
Abstract
A compound option is simply an option on an option. The valuation formulas of European-style compound options can be used to provide analytic approximations to American option values.
Thursday, April 14, 2005
| Topic |
A Closed-Form Solution for Options with Stochastic Volatility |
| Speaker |
Irena Andreevska |
| Time |
11:00-12:00 p.m. |
| Place |
PHY 013 |
Abstract
A closed-form solution of the derivative pricing partial differential equation will be derived. The model allows arbitrary correlation between volatility and the spot asset's price. The solution technique is based on characteristic functions.
Thursday, March 31, 2005
| Topic |
Credit Default Swap: Bond Price-Based Pricing |
| Speaker |
Michiru Shabata |
| Time |
11:00-12:00 p.m. |
| Place |
PHY 013 |
Abstract
In this model, it is assumed that the actual market price of bonds reflects the survival/default rate of the issuer. Under this assumption, the price of credit default swap is analysed using discrete time blocks.
Thursday, March 23, 2005
| Topic |
Stochastic Volatility Models and Derivative Pricing Under Stochastic Volatility |
| Speaker |
Irena Andreevska |
Time |
11:00-12:00 p.m. |
| Place |
PHY 013 |
Abstract
The original Black-Scholes model relates derivative prices to currents stock prices and quantifies risk using constant volatility parameter. However, the empirical studies of the stock-price changes lead to modeling the volatility as a stochastic process. Several existing stochastic volatility models will be introduced. The derivative pricing partial differential equation will be derived under the assumption that the volatility is a function of a mean-reverting Ornstein-Uhlenbeck process.
Thursday, March 3, 2005
| Topic |
Analysis of Lookback Quantos |
| Speaker |
Djiby Fall |
| Time |
11:00-12:00 p.m. |
| Place |
PHY 013 |
Abstract
Lookback quantos are contingent claims whose payoff depends on the extreme
values of the underlying cross-currency exchange rates within the lifespan.
The analytic valuation formulas of European quantos are derived along with
some considerations of American quantos.
Thursday, February 24, 2005
| Topic |
Credit Derivatives — Overview |
| Speaker |
Michiru Shibata |
| Time |
11:00-12:00 p.m. |
| Place |
PHY 013 |
Abstract
Credit derivatives were introduced in the financial market in 1990s. Its market has been expanding exponentially and some market participants expect it to be a possible financial stabilizer. In this talk, overview of credit derivatives will be given, along with some examples (and hedge-based pricing, if time permits).
Thursday, February 17, 2005
| Topic |
American Options as Free Boundary Problems, Part II |
| Speaker |
Elena Valkanova |
| Time |
11:00-12:00 p.m. |
| Place |
PHY 013 |
Thursday, February 10, 2005
| Topic |
American Options as Free Boundary Problems |
| Speaker |
Elena Valkanova |
| Time |
11:00-12:00 p.m. |
| Place |
PHY 013 |
Abstract
The valuation of American option requires a system of boundary and final conditions. At each time the holder of the option has to determine not only the option value, but also to hold or to exercise the option.
One approach is to first find a closed form solution to the Black-Scholes equation in terms of the free boundary curve, and then to obtain the optimal exercise curve for American call option. The valuation formula is derived by using the equilibrium condition, or that the expected return on a hedged position must be equal to the return on a riskless asset.
Thursday, February 3, 2005
| Topic |
A framework for path-dependent options, Part II |
| Speaker |
Yuncheng You |
| Time |
11:00-12:00 p.m. |
| Place |
PHY 013 |
Thursday, January 27, 2005
| Topic |
A framework for path-dependent options |
| Speaker |
Yuncheng You |
| Time |
11:00-12:00 p.m. |
| Place |
PHY 013 |
Abstract
Concerning the valuation of path-dependent options, we shall talk about the generalized Black-Scholes equations, discrete sampling, and similarity reductions for the general framework and the Asian averaging strike options.