To provide one motivation for the development of ARCH models (next handout), we briefly discuss here some difficulties associated with the Black Scholes formula, which is widely used to calculate the price of an option. For example, consider a European call option for a stock. This is the right to buy a specific number of shares of a specific stock on a specific date in the future, at a specifi...

We study the eeect of stochastic volatility on option prices. In the fast-mean reversion model for stochastic volatility of 5], we show that there is a full asymptotic expansion for the option price, centered at the Black-Scholes price. We show, however, that this price does not converge in a strong sense to Black-Scholes as the mean-reversion rate increases. We also introduce a general (possib...

We extend Graham’s (1981) welfare analysis under uncertainty to a dynamic environment where the agent can delay and obtain information. The dynamic willingness to pay locus unifies the concepts of option price, dynamic WTP, commitment costs and quasi-option value. Option price (dynamic WTP) corresponds to the ex ante WTP when the agent ignores (recognises) the learning opportunity. The commitme...

This article examines the influences of two forms of buyout options – permanent (i.e., a buyer could buy out the item at any point during the entire bidding process) and temporary (i.e., buyout option ceases to be present once the bidding price exceeds the reserve price) – under the presence of reserve price on a buyer’s decision in online auctions. We propose that the presence of permanent buy...

Following the economic rationale of [10] and [11] we present a new class of lookback options (by first studying the canonical ‘Russian’ variant) where the holder enjoys the early exercise feature of American options whereupon his payoff (deliverable immediately) is the ‘best prediction’ of the European payoff under the hypothesis that the true drift of the stock price equals a contract drift. I...

Following the economic rationale of [7] and [8] we present a new class of Asian options where the holder enjoys the early exercise feature of American options whereupon his payoff (deliverable immediately) is the ‘best prediction’ of the European payoff under the hypothesis that the true drift of the stock price equals a contract drift. Inherent in this is a protection feature which is key to t...

In this paper, we use Mellin transform to get the expression for the free boundary an price of an American finite-lived option, when the underlying is govern by the Levy process. We have also derived the free boundary and price of an American perpetual put as the limit of the preceded finite-lived option. We then show how to compute the price of an American option on a basket of stocks using Me...

• Incorporation of price risk into decision making process is fundamentally important. Both historical price information and projected future price come into play. Due to the usual lengthy gap between planning and harvest, expected price is the dominant factor. Given that many agricultural commodities are represented in the future and option markets, it is a common practice to infer the collect...