{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Lecture 19-21 - Options II 1.Binomial Option Pricing 1.1...

Info icon This preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
Lily Qiu, Assistant Professor Economics Department, Brown University EC1710, Lecture 19-21, Spring 2010, page 1 Options, II 1.Binomial Option Pricing 1.1 Let’s start with a simple example: assume S 0 = $100 at the beginning of the year, the price of the stock can go up to $110 at the end of the year (by a factor of u=1.1), or drop to $90 (by a factor of d=0.9). A call option on this stock has an exercise price of $105 and a time to expiration of 1 year. The risk-free annual interest rate is 5%. Let’s use value “trees” to illustrate the payoffs: Stock Option / / 100 C 0 \ \ Now, we also form a leveraged portfolio. We buy one share at the beginning of the year at $100, borrow $85.71 at the 5% to finance the purchase. Its value tree at the end of the year: Leveraged portfolio / 14.29 \ If we buy 4 call options, we have the same cashflow pattern as the leveraged portfolio, then it must be that the cost of buying 4 call options is the same as the cost of constructing the leveraged portfolio: 4C 0 = 14.29 => C 0 = $3.57 REMARK: This method of constructing a portfolio consisting of the risk-free and the underlying asset, which mimics the cashflow pattern of the option, is called replication => important concept behind most option pricing formulas. We can also create a perfect hedge by buying one share and write 4 calls. Portfolio value / $110 $20 = $90 $100 - $14.29 = $85.71 \ $90 0 = $90
Image of page 1

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

View Full Document Right Arrow Icon
Lily Qiu, Assistant Professor Economics Department, Brown University EC1710, Lecture 19-21, Spring 2010, page 2 The portfolio is risk-less => a perfect hedge , it earns the risk-free return of 5%: $85.71 * 1.05 = $90. The hedge ratio = hedge perfect the in options of number the hedge perfect the in shares of number the _ _ _ _ _ _ _ _ _ _ _ _ _ _ => 1/4 in this example.
Image of page 2
Image of page 3
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