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Mathematics & Statistics

Applied Mathematics and Finance
(Leader: Prof. Yuncheng You )

Thursday, April 21, 2005

Title
Speaker
Time
Place

The Valuation Formulas for Compound Options
Elena Valkanova
11:00am-12:00pm
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

Title
Speaker
Time
Place

A Closed-Form Solution for Options with Stochastic Volatility
Irena Andreevska
11:00am-12:00pm
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

Title
Speaker
Time
Place

Credit Default Swap: Bond Price-Based Pricing
Michiru Shibata
11:00am-12:00pm
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

Title
Speaker
Time
Place

Stochastic Volatility Models and Derivative Pricing Under Stochastic Volatility
Irena Andreevska
11:00am-12:00pm
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

Title
Speaker
Time
Place

Analysis of Lookback Quantos
Djiby Fall
11:00am-12:00pm
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

Title
Speaker
Time
Place

Credit Derivatives — Overview
Michiru Shibata
11:00am-12:00pm
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

Title
Speaker
Time
Place

American Options as Free Boundary Problems, Part II
Elena Valkanova
11:00am-12:00pm
PHY 013

Thursday, February 10, 2005

Title
Speaker
Time
Place

American Options as Free Boundary Problems
Elena Valkanova
11:00am-12:00pm
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

Title
Speaker
Time
Place

A framework for path-dependent options, Part II
Yuncheng You
11:00am-12:00pm
PHY 013

Thursday, January 27, 2005

Title
Speaker
Time
Place

A framework for path-dependent options
Yuncheng You
11:00am-12:00pm
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.