6_FuturesOptions_update.pdf

# L payoffs at t1 33 30xye 00612 4 xye 00612 0 x08 and

• Notes
• 49

This preview shows pages 44–49. Sign up to view the full content.

l Payoffs at t=1 : ( 33-30)x+ye 0.06/12 =4 and (28-30)x+ye 0.06/12 =0 x=0.8 and y=1.592 l Cost of the portfolio at t=0 : 1.592 l This is the price of the futures option. Method 2: Setting up a replicating portfolio 44

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

Overview 1. Definition 2. Settlement procedures 3. Valuation using binomial trees 4. Valuation using Black’s model Fin330 45
l The formula for the European option on futures is known as Black’s model. l For a European option written on a futures contract, we use an adjustment of the Black-Scholes solution, which was developed in Black (1976). l Essentially we replace S 0 with e -rT F 0 in the Black-Scholes formula. Fin330 46 Black’s Model

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

Fin330 Black’s Model c = N ( d 1 ) Ke rT N ( d 2 ) p = Ke rT N ( d 2 ) N ( d 1 ) where d 1 = ln( F 0 / K ) + σ 2 T / 2 σ T d 2 = ln( F 0 / K ) σ 2 T / 2 σ T = d 1 σ T 47
Black’s model: Numerical example l A European put futures option. l Option matures is 4 months. l Current futures price is \$60. l Strike price is \$60. l Annual (cont. comp.) interest rate is 9%. l Volatility of the futures price is 25% per annum. l Find the price of the put p . Fin330 48

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

l F 0 =60, K=60, r=0.09, T=4/12, σ =0.25 . l d 1 =0.07216 l d 2 =-0.07216 l N(-d 1 )=0.4712 l N(-d 2 )=0.5288 l p=e -0.09x(4/12) (60x0.5288 – 60x0.4712)=3.35 Fin330 49 Black’s model: Numerical example
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern