Part I proposes a numeraire-invariant option pricing framework. It defines an option, its price process, and such notions as option indistinguishability and equivalence, domination, payoff process, trigger option, and semipositive option. It develops some of their basic properties, including price transitivity law, indistinguishability results, convergence results, and, in relation to nonnegati...

a r t i c l e i n f o This paper examines the relationship between option trading activity and stock market volatility. Although the option market is uniquely suited for trading on volatility information, there is little analysis on how trading activity in this market is linked to stock price volatility. The bulk of the discussion tends to focus on whether trading activity in the stock market i...

We analyze and explore option fragility, the notion that option incentives are fragile due to their non-linear payoff structure. Option incentives become weaker as options fall underwater, leading to pressures to reprice options or restore incentives through additional grants of equitybased pay. We build a detailed data set on executives’ portfolios of stock and options and find that executive ...

To have a real option means to have the possibility for a certain period to either choose for or against making an invetsment decision, without binding oneself up front. The real option rule is that one should invest today only if the net present value is high enough to compensate for giving up the value of the option to wait. Because the option to invest loses its value when the investment is ...

We develop a new method for pricing American options. The main practical contribution of this paper is a general algorithm for constructing upper and lower bounds on the true price of the option using any approximation to the option price. We show that our bounds are tight, so that if the initial approximation is close to the true price of the option, the bounds are also guaranteed to be close....

In an auction with a buy price, the seller provides bidders with an option to end the auction early by accepting a transaction at a posted price. The ”BuyIt-Now” option on eBay is a leading example of an auction with a buy price. This paper develops a model of an auction with a buy price in which bidders use the auction’s reserve price and buy price to formulate a reference price. The model bot...

We find that weekend, holiday and overnight trading breaks generate excessive perceived risk in the option markets, presumably due to asymmetric information, which, in turn, encourages uninformed option traders to postpone trading. This perceived risk subsides after two days accompanied by an increase in the option trading volume and the underlying index’s actual price volatility. These results...

I examine the role of programming parameters in determining the accuracy of Genetic Programming for option pricing. I use Monte Carlo simulations to generate stock and option price data needed to develop a Genetic Option Pricing Program. I simulate data for two different stock price processes – a Geometric Brownian process and a JumpDiffusion process. In the jump-diffusion setting, I seed the G...

This paper will derive the Black-Scholes pricing model of a European option by calculating the expected value of the option. We will assume that the stock price is log-normally distributed and that the universe is riskneutral. Then, using Ito’s Lemma, we will justify the use of the risk-neutral rate in these initial calculations. Finally, we will prove put-call parity in order to price European...

Mathematical finance (or financial engineering, as it is often known) is a young subject for mathematics, but is highly popular with students. No doubt the allure of being connected to vast sums of money is a part of the attraction. Yet it is a difficult subject, requiring a broad array of knowledge of subjects that are traditionally considered hard to learn. Forty years ago, options and what a...