MFE Lesson 11 slides - Lesson 11 The Black-Scholes formula...

Info icon This preview shows pages 1–9. Sign up to view the full content.

View Full Document Right Arrow Icon
Lesson 11: The Black-Scholes formula: applications and volatility. ACTS 4302 Natalia A. Humphreys October 11, 2012 1 / 25
Image of page 1

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

View Full Document Right Arrow Icon
Acknowledgement This work is based on the material in ASM MFE Study Manual for Exam MFE/Exam 3F. Financial Economics (7th Edition), 2009, by Abraham Weishaus. 2 / 25
Image of page 2
What we’ll study In this section we’ll study how profit evolves on an option as time passes. We’ll also determine how to calculate the volatility that is implied in the BS formula. 3 / 25
Image of page 3

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

View Full Document Right Arrow Icon
Profit diagrams before maturity As a European option ages, time to expiry decreases. A 91-day European option that is 5 days old is equivalent to an 86-day European option, so we can track the price of options using the BS formula. 4 / 25
Image of page 4
Call options and bull spreads Let C T be the price of a call option with expiry time T . Suppose after time t the purchaser decided to sell it. Then the profit they made on this call is the change in call premiums at time T - t , that is the di erence between the final value of the call and the initial value of the call grown with interest:: Profit = C T - t - C T e rt If the time to expiry is measured in days, the formula will change to: Profit = C T - t - C T e rt / 365 5 / 25
Image of page 5

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

View Full Document Right Arrow Icon
Example 11.1 You are given: (i) The price of a stock is 55. (ii) The stock’s continuous dividend rate is 0.01. (iii) The volatility of the stock is 0.1. (iv) A 182-day European call has strike price 56. (v) The continuously compounded risk-free rate is 0.05. Calculate the 10-day holding period profit on the call if the stock’s price is 56 at the end of 10 days. 6 / 25
Image of page 6
Example 11.1. Solution. d 1 = ln 55 56 + (0 . 05 - 0 . 01 + 0 . 5 · 0 . 1 2 ) 182 365 0 . 1 q 182 365 = 0 . 0626 d 2 = 0 . 0626 - 0 . 1 r 182 365 = - 0 . 0080 N ( d 1 ) = N (0 . 06) = 0 . 5239 , N ( d 2 ) = N ( - 0 . 01) = 0 . 4960 e - rt = e - 0 . 05 · 182 365 = 0 . 9754 e - δ t = e - 0 . 01 · 182 365 = 0 . 9950 C = 55 · 0 . 9950 · 0 . 5239 - 56 · 0 . 9754 · 0 . 4960 = 1 . 578 7 / 25
Image of page 7

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

View Full Document Right Arrow Icon
Example 11.1. Solution (cont.) After 10 days, the BS price is: d 1 = ln 56 56 + (0 . 05 - 0 . 01 + 0 . 5 · 0 . 1 2 ) 172 365 0 . 1 q 172 365 = 0 . 3089 d 2 = 0 . 3089 - 0 . 1 r 172 365 = 0 . 2403 N ( d 1 ) = N (0 . 31) = 0 . 6217 , N ( d 2 ) = N (0 . 24) = 0 . 5948 e - rt = e - 0 . 05 · 172 365 = 0 . 9767 e - δ t = e - 0 . 01 · 172 365 = 0 . 9953 C = 56 · 0 . 9953 · 0 . 6217 - 56 · 0 . 9767 · 0 . 5948 = 2 . 119
Image of page 8
Image of page 9
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    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.

    Student Picture

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

  • Left Quote Icon

    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.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    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.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern