{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Lecture23

# Lecture23 - • Investor writes one call and buys H shares...

This preview shows pages 1–14. Sign up to view the full content.

Lecture 23 : Options Markets Economics 252, Spring 2008 Prof. Robert Shiller, Yale University

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Put-Call Parity Relation Put option price – call option price = present value of strike price + present value of dividends – price of stock For European options, this formula must hold (up to small deviations due to transactions costs), otherwise there would be arbitrage profit opportunities

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Binomial Option Pricing S = current stock price u = 1+fraction of change in stock price if price goes up d = 1+fraction of change in stock price if price goes down r = risk-free interest rate

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Binomial Option Pricing, Cont. C = current price of call option C u = value of call next period if price is up C d = value of call next period if price is down E = strike price of option H = hedge ratio, number of shares purchased per call sold
Hedging by writing calls

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: • Investor writes one call and buys H shares of underlying stock • If price goes up, will be worth uHS-C u • If price goes down, worth dHS-C d • For what H are these two the same? Binomial Option Pricing Formula • One invested HS-C to achieve riskless return, hence the return must equal (1+ r) ( HS-C ) • (1+ r )( HS-C )= uHS-C u = dHS-C d • Subst for H , then solve for C Black-Scholes Option Pricing Call T the time to exercise, σ 2 the variance of one-period price change (as fraction) and N(x) the standard cumulative normal distribution function (sigmoid curve, integral of normal bell-shaped curve) =normdist(x,0,1,1) Excel (x, mean,standard_dev, 0 for density, 1 for cum.) Black-Scholes Formula Actual S&P500 Volatility Monthly July1871- April 2008 Implied and Actual Volatility Monthly Jan 1986-April 2008...
View Full Document

{[ snackBarMessage ]}

### Page1 / 14

Lecture23 - • Investor writes one call and buys H shares...

This preview shows document pages 1 - 14. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online