Description: In this paper we study the pricing of financial options and contingent claims. We show that two time-honored concepts in actuarial science - the Esscher transform and the adjustment coefficient - are efficient tools for pricing many options and derivative securities if the logarithms of the prices of the primitive securities are certain stochastic processes with stationary and independent increments. We also study the pricing of American options on two stocks without expiration date and with payoff functions which are homogeneous with respect to the two stock prices.

Description: This paper examines the pricing of catastrophe risk bonds. Catastrophe risk cannot be hedged by traditional securities. Therefore the pricing of catastrophe risk bonds requires an incomplete markets setting and this creates special difficulties in the pricing methodology. The paper briefly discusses the theory of equilibrium pricing and its relationship to the standard arbitrage-free valuation framework. Equilibrium pricing theory is used to develop a pricing method based on a model of the term structure of interest rates and a probability structure for the catastrophe risk. This pricing methodology can be used to assess the default spread on catastrophe risk bonds relative to traditional defaultable securities.

Description: This is the abstract of the paper 'A Stochastic Definition of Future Shares'. The traditional definition of actuarial future values and stochastic definition of Ramsay are discussed. A modification of Ramsay's definition is proposed and an application to life insurance reserves is presented.

Description: This paper proposes to put the environment into financial markets. It explains how to do it, and why the financial approach is practically the only one able to stop and invert environmental degradation. The author concentrates on deforestation which is the largest environmental problem in the third world, and explains how to start the project and what kind of optimization problems should be solved for applications of the project.

Description: In 1993, the Chicago Board of Trade introduced a futures contract on a financial index that reflects the insurance claims emerging from catastrophes in a portfolio of policies. This article presents a valuation formula for the contract, under the assumption that catastrophes emerge as a Poisson process over time and that the claims from each catastrophe emerge as a Compound Poisson process. The formula is developed by taking conditional expectations with respect to a history of information that includes knowledge about the time of the catastrophes.

Description: One of the most important problems in Finance is the valuation of financial securities written on underlying assets whose prices are subject to uncertainty. This paper presents a technique to estimate the unknown stochastic volatilities by solving the inverse problem associated with the parabolic partial differential equation governing risk neutral derivative security prices. This technique can be applied in a very general multi-factor setting and numerical examples are provided.

Description: This is the abstract of the paper Quasi-Monte Carlo Methods in Numerical Finance. This paper introduces and illustrates a new version of the Monte Carl method that has attractive properties for the numerical valuation of derivatives. The traditional Monte Carlo method has proven to be a powerful and flexible tool for many types of derivatives calculations.

Description: These are the abstract and reference of the paper 'Bounds on Multiple Contingent Claims'. Lo considered the problem on bounding a European option on a single asset. He obtained an upper bound on the payoff of the European call in terms of the mean and variance of the underlying asset. In this talk, we extend Lo's result to the multi-asset case. Unlike the one asset case, the correlations between the assets play an important role and have to be taken into consideration.

Description: This is the abstract of the paper 'Pricing of Credit Derivatives'. This talk will give an overview of current pricing techniques. We first show how to build a credit curve. A credit curve gives the instantaneous default probability of a party at any time in the future. It is as important to credit derivative pricing as the yield curve is to fixed income derivative pricing.

Description: This note develops the optimality of the put option as a hedging strategy. For an investor who owns a stock, he can buy a put option to hedge against the downside risk of the stock price. In this short note, we ask two questions with the hedge strategy of the put option. First, whether the investor is better off with the hedging strategy? Second, if the investor is better off with the hedging strategy, whether it is the optimal hedging plan? Our result shows that in a risk averse world an investor will maximize his utility with buying the put option as a hedge strategy.