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BRIEF INTRODUCTION

Attempts to explain the crash in the stock market around the world in

October 1987

Reason cited was the major economic developments took place around

that time

Alternative hypothesis: reason behind crash because it was expected to

crash (Rational Bubble)

Bianchard and Watson (1992) model of a rational bubble

Approach taken in was that Marketswas overvalued,hence expected to

crash

Alternative approach of using Options Prices decline whether a crash was

expected

Out of the money puts which provide crash insurance, were unusually

expensive then the out-of-the-money calls.

A jump-diffusion model fitted to option prices during 1987, and expected

negative jumps invariably found prior to crash.

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THEORETICAL FOUNDATIONS

Fundamental to the pricing of options Derivation from the actual

distribution of the asset price of an equivalent riskneutraldistribution

that summarizes the prices of relevant

Options priced at discounted expected value of their future payoffs

Most of the standard specifications of the models can be inconsistent with

observed option prices

Implication of the models suggest OTM puts should trade at slight

discount relative to OTM calls, contrary to fact

The parameters of the riskneutralprocess implicit (via non linear least

squares):

The volatility conditional on no jumps, Probability of jump

The mean jump size conditional

The standard deviation of jump sizes

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Theoretical work is summarized concerning the relationship between

OTM call and put option prices for standard distributional hypotheses.

Most of the specifications of these models were ruled out a priori as

inconsistent with observed option prices.

This imply that OTM puts should trade at a slight discount relative to OTM

calls.

Because of this, transactions prices for American options of S&P 500

futures indicate either that market participants expected substantial

negative jumps(i.e. crashes) in the market during the year preceding the

crash or that they thought market volatility would rise rapidly if the

market fell.

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ESTIMATION Stochastic Differential equation

dS/S = [ - kbardt]dt + SDdZ + kdq

Where,

= instantaneous cum dividend expected return on the asset

dt = flow rate

Sd= instantaneous variance on no jumpsZ = Standard Weiner Process

k = random percentage jump conditional jump upon a Poisson

distributed event

= the frequency of Poisson events

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SUMMARY AND CONCLUSIONS Strong perception of downside risk on the market during the year

preceding the stock market crash

Program trading strategies

Portfolio insurance

Macroeconomic causes included international disputes about foreignexchange and interest rates, and fears about inflation.

Two methods were used

OTM puts which provide crash insurance were unusually expensive toOTM Calls

A jump diffusion model was fitted to daily options prices in 1987 and

expected negative jumps were invariably found starting a year prior to

crash