CM

O-MSF-FIN-521-Option-Contracts-Part-2-transcription

Investment Analysis: Options Contracts - Binomial Model

Introduction

  • Instructor: David Zynda

  • Course: FIN 521 Investment Analysis

  • Focus: Option Contracts and Binomial Model for pricing options in financial markets.

Binomial Option Pricing Model

  • Definition: Two-state model for option valuation considering up (U) and down (D) movements in stock prices.

  • Forecasting: Expected future prices calculated using percentage changes for U and D. Consistency across subperiods essential for reliable forecasting.

Price Diagram Representation

  • Visualizes stock price movements, with calculations based on sequential multiplications of U or D.

  • Probabilities: Upward movement probability (P) is 51%, downward is 49%. Influences of stock volatility on price changes.

Option Value Calculation

  • Formula: Cj = P * Cjj + (1 - P) * Cjj, where Cj is option value at state j.

  • Highlights backward calculation for present option values using recursive methods.

Generalizing the Binomial Model

  • Pricing options at Date 0: C0 = sum(N!/(N - j)!j! * P^j * (1 - P)^(N - j) * max(0, [U^j * D^(N - j) * S - X]))/R^N.

  • Hedge Ratio: Provides insights into option pricing risk management.

Practical Excel Implementation

  • Example scenario calculations involving stock price, strike price, risk-free rate, and movement percentages.

Simulating Stock Price Forecasts

  • Build price trees for expected stock prices across intervals. Use recursive calculations to derive expected values and call payoffs.

Call Pricing and Hedge Ratio Calculation

  • Backward calculation for option value based on derived payoffs and hedge ratios for risk assessment.

Conclusion

  • The Binomial Model is foundational for developing advanced pricing models like Black-Scholes, enhancing precision in option valuation.