FINS3635 Mid Sem Assignment - Sprint Certificate

20 Found helpful • 19 Pages • Essays / Projects • Year: Pre-2021

Structured products case study for Options, Futures and Other Derivatives : Sprint Certificates. The questions are : Plot the payo in USD of this structured product as a function of the stock price S(T) at maturity. Consider values for S(T) in the range from 0.00 USD to 200.00 USD. b) Give a formula for the payo of the sprint certicate as a function of the stock price S(T) at maturity. c) The payo of the sprint certicate can be replicated by taking positions in zero-coupon bonds and/or the underlying asset and/or various options. Propose one such portfolio and show that the payo function of this portfolio is equal to the payo function of the sprint certicate. d) Propose a second portfolio that replicates the payo of the sprint certicate and again show that its payo function is equal to that of the sprint certicate. e) Describe the market view that an investors who buys this structured product today and plans to hold it until the maturity date should have. I.e. what is his expectation for the stock price S(T) at maturity? You need to give details justify your answer. Hint: Making a simple statement like \He expects the stock to increase/decrease/stay the same." is not sucient. f) Assume that all Cox-Ross-Rubinstein assumptions holds. The volatility of FINS3635 Stu- dent Corp. is 25% p.a., the continuously compounded risk-free interest rate is 10% and 2 there are no dividends. Compute the price of one sprint certicate in a two-step Cox-Ross- Rubinstein binomial tree using the results from either part c) or d). Note that this will only be a very crude approximation to the Black-Scholes price that you compute in part g). Hint: Note that this will only be a very crude approximation to the Black-Scholes price that you compute in part g). g) Assume that all Black-Scholes assumptions hold and use the market data from part f). Compute the (i) price, (ii) delta, (iii) gamma, (iv) vega and (v) theta of one sprint certicate using the results from either part c) or d). h) How would the price of the sprint certicate change if FINS3635 Student Corp. announced that it would pay a (non-zero) dividend in half a year? Argue without computations. Hint: As usual, when analyzing sensitivities we make a ceteris paribus assumption. In particular, the stock price is assumed not to change due to the dividend announcement. i) Consider the same situation as in part g) but now assume that the stock price instantaneously jumps to S(0) = 105:00 USD. (i) Explicitly compute the new price of the sprint certicate and compare it to the result in part g). Explain (ii) the sign of the change and (iii) the magnitude of the change. (iv) Approximate the price change of the sprint certicate using its Black-Scholes delta from part g) and explain why the approximation over-/under-estimates the actual price change. j) Consider the same situation as in part g) but now assume that the volatility instantaneously jumps to 30% p.a.. (i) Compute the new price of the sprint certicate and compare it to the result in part g). (ii) Explain the sign of the change.

This document is 10 Exchange Credits