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11 12 09 Review Session 9 _Concept Review_

# 11 12 09 Review Session 9 _Concept Review_ - Managerial...

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Managerial Finance: Review Session 9 TA: Pablo Villanueva December 9, 2011

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Agenda for Today 1. Option Valuation Binomial Tree (last week’s Review Session). Black-Scholes Formula. Black-Scholes Formula with Dividends. Risk Neutral Probabilities. 2. Application to Corporate Finance.
Black-Scholes Formula 1. Black-Scholes formula gives us a (easy) way to price options (same intuition as Binomial Tree) 2. The formula works for Calls with no dividends (and can be adapted to European puts with no dividends). C = S * N ( d 1 ) - PV ( K ) N ( d 2 ) (1) d 1 = ln [ S PV ( K ) ] σ T + σ T 2 (2) d 2 = d 1 - σ T (3)

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Black-Scholes Formula: Interpretation 1. d 1 is the percentage of the stock that we need to hold to replicate the portfolio. 2. d 2 is the percentage of a zero bond with face value of K that we need to short to replicate the portfolio. 3. Exercises 21.11, 21.17, 21.18
Black-Scholes Formula with Dividends 1. If dividends are paid proportional to the Stock price and q is the stock’s dividend yield until expiration date, we can use the

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11 12 09 Review Session 9 _Concept Review_ - Managerial...

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