Implied risk-neutral probability density functions from option prices: theory and application

Contents

Abstract

1 Introduction

2 The relationship between option prices and RND functions

2.1 Pricing elementary claims from option prices

2.2 The Black-Scholes (1973) formula and its RND function

2.3 The implied volatility smile curve

3 Some techniques for estimating implied terminal RND functions

3.1 A simple approach: risk-neutral histograms

3.2 Interpolating the call option pricing function directly

3.3 Interpolating the implied volatility smile curve

3.4 Fitting an assumed option pricing model to observed

option prices

3.5 Fitting an assumed parametric form for the implied RND

function to observed option prices

3.6 Application of the two-lognormal mixture approach to

equity, interest rate and foreign exchange markets

a) LIFFE equity index options

b) LIFFE options on short interest rate and long bond futures

c) Philadelphia Stock Exchange (PHLX) currency options

4 Using the information contained in implied RND functions

4.1 Summary statistics

4.2 Validation

4.2.1 Analysing changes in implied RND functions over time

4.2.2 Analysing changes in implied RND functions around

specific events

4.3 Use of implied RND functions by monetary authorities

4.3.1 Assessing monetary conditions

4.3.2 Assessing monetary credibility

4.3.3 Assessing the timing and effectiveness of monetary

operations

4.3.4 Identifying market anomalies

5 Data limitations

6 Conclusions

Mathematical appendix

References

[此贴子已经被作者于2006-1-17 10:04:34编辑过]