How would one replicate an option with the following payoffs:I will give you $1500 today. In return, you have to guarantee to pay me in two years time whatever the square of the stock price is at that time. (ex. if Stock ABC = $80, the payoff is $6400).The current stock price is $20, r = 22.31%, and the stock price can either increase by 100% or decrease by 50% each year.No dividends.Thanks!

Thanks. What is it that I differentite wrt s? Also, how do I find B? Thanks.

QuoteOriginally posted by: swapsterHow would one replicate an option with the following payoffs:I will give you $1500 today. In return, you have to guarantee to pay me in two years time whatever the square of the stock price is at that time. (ex. if Stock ABC = $80, the payoff is $6400).The current stock price is $20, r = 22.31%, and the stock price can either increase by 100% or decrease by 50% each year.No dividends.Thanks!Sorry, I misread your question, so ignore what I said before.What you have here is two-step binomial tree. Start at year one. The stock price has two possible values after one year. Choose one.To hedge the payoff, you need to set up a portfolio of x stocks and y zero coupon bonds. The bond will have a value of 1 at the payoff time so you should be able to calculate the value at all earlier times. The stock after one more year has two possible values giving your portfolio two possible values. The idea is to choose x and y to ensure that the two possible values are equal to the two possible payoffs. If you write this condition down you will get a set of linear equations which you can solve for x and y. Now you know the number of stocks and bonds you need to be holding and therefore the value of the portfolio, if the stock takes the value you chose after one year.Now repeat for the other possible value.Now you have a portfolio which must take two possible values after one year. To find its value now, and the number of stocks and bonds you need to hold now, just repeat the procedure again. The stock can take two values, the portfolio must be equal to the value you calculated for each of these possibilities. This gives a set of linear equations etc.I recommend you read something like chapter 2 of Financial Calculus by Baxter and Rennie, they explain this much better than I have and its so much easier with diagrams.

Thanks everyone.

piece-wise linear approx.Figure out home many callspreads you need to hedge each part of the approx. Figure out home much those callspreads cost. Add em up. Converges faster that a tree cause it's one dim.

most importantly it is easy to price skew

It is a power option ... somewhat strange, that your stock knows his future :-)But if you accept that the price will at most 80 in 2 years you can take this asa cap, strike is 0 and pay off max(spot-strike)^2 = strike^2. To replicate youcan buy N calls with strike N (and maturity 2 y), N <= 80 , summing them up islike summing the first 80 numbers (if one is left or lost figure it out exactly).Estimating vol is a job left to you Otherwise do it as binomial tree. edited: ääää ... max(spot-strike)^2 = spot^2

Your answer here:http://www.math.nyu.edu/research/carrp/ ... ingoh1.pdf

mad post.just take discounted risk neutral expectationeg 6400,400,400,25 are the payoffs of the optionso discount the payoffget1207.4 as being the value.

The original questions been asked a lot in different guises. If some one says here's 1500 bucks for that contract I say great cause it's worth 576.05.The thing runs two years and the distribution is known.Payoff80 = 640020 = 4005 = 25after the first year the stock can be 40 or 10 so going back you see the delta at 40 is (6400-400)/60 = 100 so the value of the contract is 2400*exp(-22.31%) ~ 1920.08. Similar calculations lead you to believe that the value at 10 is 120. Do same thing to get back to 20 start time and you'll probably get my number.

QuoteOriginally posted by: worowpiece-wise linear approx.Figure out home many callspreads you need to hedge each part of the approx. Figure out home much those callspreads cost. Add em up. Converges faster that a tree cause it's one dim.worow,could you elaborate a bit on this ? I think I missed your point. Thanks.