Compute the black-scholes price of one reverse convertible , Finance Basics

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Case Study: Reverse Convertible Bond

Initial Reference Level: 50.00 USD

Final Reference Level: The offcial closing price of the Underlying on the Maturity Date.

a) If the Final Reference Level is at or above the Strike price, a cash redemption amount equal to the Notional plus Coupon.

b) If the Final Reference Level is below the Strike price, a cash redemption amount equal to the Coupon plus physical delivery of 2.5 Underlying shares.

The current price of one share of FINS3635 Student Corp. is equal to S(0) = 50:00 USD.

a) Plot the payoff in USD (incl. the coupon payment) 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 100.00 USD.

b) Give a formula for the payoff of the reverse convertible bond (incl. the coupon payment) as a function of the stock price S(T) at maturity.

c) The payoff of the reverse convertible bond can be replicated by taking positions in zero-coupon bonds and/or the underlying asset and/or various options. Propose one such port-folio and show that the payoff function of this portfolio is equal to the payo_ function of the reverse convertible bond.

d) Propose a second portfolio that replicates the payoff of the reverse convertible bond and again show that its payoff function is equal to that of the reverse convertible bond.

e) Assume that the continuously compounded risk-free interest rate is 10%. Based on your above analysis, will the current price of the reverse convertible bond be lower, equal to, or higher than its notional value? You need to justify your answer using the results from either part c) or d).

f) Using the risk-free interest rate given in part e) and the results from either part c) or d), compute the upper and lower bound for the current price of the reverse convertible bond.

g) 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 justify your answer.

h) Assume that all Cox-Ross-Rubinstein assumptions holds. The volatility of FINS3635 Student Corp. is 30% p.a., the continuously compounded risk-free interest rate is 5% and there are no dividends. Note that the risk-free interest rate is di_erent from the one used in part e). Compute the price of one reverse convertible bond in a two-step Cox-Ross-Rubinstein binomial tree using the results from either part c) or d). i) Assume that all Black-Scholes assumptions hold and use the market data from part h).

Compute the Black-Scholes price of one reverse convertible bond using the results from either part c) or d).

j) Consider the same situation as in part i) but now assume that the stock price instantaneously jumps to S(0) = 52:50 USD. Compute the new price of the reverse convertible bond and compare it to the result in part i). Explain i) the sign of the change and ii) the magnitude of the change. Approximate the price change of the reverse convertible bond using its delta and explain why the approximation over-/under-estimates the actual price change.

k) Consider the same situation as in part i) but now assume that the volatility instantaneously jumps to 35% p.a.. Compute the new price of the reverse convertible bond and compare it to the result in part i). Explain the sign of the change.


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