Derivatives09-5 - The Greek Letters

# Derivatives09-5- - Session 6 The Greek Letters Example(Page 325 • A bank has sold for \$300,000 a European call option on 100,000 shares of a

This preview shows pages 1–11. Sign up to view the full content.

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 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: Session 6 The Greek Letters Example (Page 325) • A bank has sold for \$300,000 a European call option on 100,000 shares of a non-dividend- paying stock • S = 49, K = 50, r = 5%, σ = 20%, T = 20 weeks, μ = 13% • The Black-Scholes value of the option is \$240,000 • How does the bank hedge its risk? Naked & Covered Positions Naked position Take no action Covered position Buy 100,000 shares today Both strategies leave the bank exposed to significant risk Stop-Loss Strategy This involves: • Buying 100,000 shares as soon as price reaches \$50 • Selling 100,000 shares as soon as price falls below \$50 This deceptively simple hedging strategy does not work well Relation between delta, gamma, theta ∂ ∂ ∂ ∂ ∂ ∂ σ f t rS f S f S S rf + + = 1 2 2 2 2 2 • Remember PDE: Theta Delta Gamma Fundamental determinants of option value Call value Put Value Current asset price S Delta C 0 < Delta < 1 C- 1 < Delta < Striking price K K K Interest rate r Rho C C Dividend yield q K K Time-to-maturity T Theta C ? Volatility Vega C C Delta (See Figure 15.2, page 329) • Delta ( ∆ ) is the rate of change of the option price with respect to the underlying Option price A B Slope = ∆ Stock price Delta Hedging • This involves maintaining a delta neutral portfolio • The delta of a European call on a non-dividend- paying stock is N ( d 1 ) • The delta of a European put on the stock is [ N ( d 1 ) – 1] Delta Hedging continued • The hedge position must be frequently rebalanced • Delta hedging a written option involves a “buy high, sell low” trading rule • See Tables 15.2 (page 332) and 15.3 (page 333) for examples of delta hedging Example BLACK-SCHOLES OPTION PRICING FORMULA A.Farber Stock price 100 Call Put Dividend yield 0.00% Decomposition of value Striking price 100 Intrinsic val. 0.00 0.00 Maturity (days) 365 Time value 4.88-4.88 Interest rate 5.00% Insurance 5.57 10.45 Volatility 20.00% BS partial differential equation Theta-6.41-1.66 Call Put (r-q)SDelta 3.18-1.82 Price 10.451 5.574 0.5 σ ²S²Gamma 3.75 3.75 Delta 0.6370....
View Full Document

## This note was uploaded on 02/21/2010 for the course FINA 221 taught by Professor Na during the Spring '09 term at HKUST.

### Page1 / 37

Derivatives09-5- - Session 6 The Greek Letters Example(Page 325 • A bank has sold for \$300,000 a European call option on 100,000 shares of a

This preview shows document pages 1 - 11. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online