Delta neutral, call & put option

[Uclmak]

Can anybody help in finding solution for the following equation:-

Q1. Consider a one year put swaption, which has an underlying swap as a four-year swap. A put swaption gives its buyer the right to enter into a swap as a floating rate payer and if he exercises the option, receives fixed rate from the swap. The strike price of the put swaption is 9% and the notional principal is $10 million. At expiration of the swaption, the spot rates on zero coupon bonds of various maturities turned out as below:

Year Yield on Zero Coupon Bond
1 7.5%
2 8.0%
3 8.4%
4 8.7%

You are required to calculate the payoff from the put swaption (Assume 360 days in a year)

Q2. An Indian Bank has sold three-month European call option on $2 million with a strike price of Rs 45.10. The current rupee dollar exchange rate is Rs 45.30/$. The annual volatility of rupee-dollar exchange rates is 6%. The 91-day T-Bill rate in India is 4% p.a and 91-day US T-Bill rate is 1% p.a.

You are required to find out the position the bank should take (using options) to make the position delta neutral.

Q3. The Current market price of ABB's stock if Rs 290. The Following European call an put options are available in the market.

Option Strike Price Premium Expiration(Months)
Call 280 24 6
Put 280 3 6
The risk-free interest rate is 6% p.a

You are required to find out whether there is any arbitrage opportunity available in the put and call prices. If no, justify why not. If yes, show how you can make arbitrage profit.

 

[Martinghoul]

Q1. Firstly, there's no such thing as a "put swaption". What you're describing is a "receiver (swaption)". At any rate, to calculate the payoff, you need to convert the zero rates to a 4y par swap rate. Once you have that it's easy to calculate the PV of the swap where you receive 9% fixed (that's what your swaption expires into). It's not entirely clear that the question is posed correctly, as you need to know whether the swaption is cash- or physical-settled. If the latter, strictly speaking there is no "payoff".

Q2. That's just trivial Black-Scholes applied to FX options, although, again, the question itself is funny.

Q3. That's just simple put-call parity. You just have to do the math to calculate the correct forward and then check if put-call parity is violated.

 

[Uclmak]

Q1. Firstly, there's no such thing as a "put swaption". What you're describing is a "receiver (swaption)". At any rate, to calculate the payoff, you need to convert the zero rates to a 4y par swap rate. Once you have that it's easy to calculate the PV of the swap where you receive 9% fixed (that's what your swaption expires into). It's not entirely clear that the question is posed correctly, as you need to know whether the swaption is cash- or physical-settled. If the latter, strictly speaking there is no "payoff".

Q2. That's just trivial Black-Scholes applied to FX options, although, again, the question itself is funny.

Q3. That's just simple put-call parity. You just have to do the math to calculate the correct forward and then check if put-call parity is violated.

Thanks Martinghoul,

For suggestion, Q1. still i am confuse, Q2 & Q3 i will be working as per suggestion