What is a binary speed option on an interval [35; 55]? Explain how you could rep

Question

What is a binary speed option on an interval [35; 55]? Explain how you could replicate the payoff of this option using simple binary options. Assume you want to borrow pound 200 for one year. The risk-free rate in the US is 5% per year, the risk-free rate in the UK is 3% per year. The spot exchange rate is S= 1.50 USD/GBP, the one year forward exchange rate is F = 1.65 USD/GBP. Explain how you can use the FX market to create a synthetic pound GBP loan. What is your potential gain or loss from using the synthetic? The investment bank you are working for wants to offer a new product with a maturity of 4 years: the Reading Note (RN). With an initial notional N, an investor in the RN would receive the following payments (where L_t, denotes the one-year LIBOR at date t): How can you synthetically create the RN by using only FRNs and Zero Bonds? Write down the replicating portfolio in a cash flow table.

Explanation / Answer

d) The binary spread option on interval[35;55] is an option that pays out a fixed amount if the underlying asset price falls between 35 and 55.Therefore there is a fixed payoff received by the binary spread option investor when the underlying asset price falls between 35 and 55.

This option can be replicated by going long on Binary option called Cash or nothing call with a strike price of 35(that pays a fixed amount $2 if the asset price rises above 35 At expiration) + going short on Cash or nothing call with a strike price of 55(that requires a fixed amount payment $2 if the asset price rises above 55 At expiration).

Therefore the payoff for these combination =Payoff on $35 strike Cash or nothing call-Payoff on $55 strike Cash or nothing call.

At expiration/maturity:

i)Asset Price<=35 ,

Payoff of combination=0-0=0(since the payoff on $35 strike Cash or nothing call is 0 since the asset price does not rise above $35, payoff on $55 strike Cash or nothing call is 0 since the asset price does not rise above $55)

ii)35<Asset Price<=55 ,

Payoff of combination=2-0 = 2 (since the payoff on $35 strike Cash or nothing call is $2 since the asset price rise above $35, payoff on $55 strike Cash or nothing call is 0 since the asset price does not rise above $55)

iii)Asset Price>55 ,

Payoff of combination=2-2= 0 (since the payoff on $35 strike Cash or nothing call is $2 since the asset price rise above $35, payoff on $55 strike Cash or nothing call is $2 since the asset price does rise above $55)

Therefore the above combination has created a fixed payoff of $2 if the asset price lies between 35 and 55.This payoff is similar and identical to the binary spread option on interval[35;55] that pays out a fixed amount if the underlying asset price falls between 35 and 55.

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