Question

For all questions, interest (r) and dividend (d) rates are continuously compounded unless specified otherwise.

r = 4%, d = 0%, T = 3 months.

a) P20 = $4.95, P18 = $2.90. Is there a possible arbitrage? If so, what is your proposed arbitrage portfolio and what is the present value of your profit?

b) Instead of being able to buy and sell the options at the same price, assume there is a bid/ask spread. P20 = $4.85/$4.95 (bid/ask) and P18 = $2.85/2.95. Now is there a possible arbitrage? What happens to the profitability of the arbitrage portfolio from a)?

explain fully please and show how it is done

Answer 1

3. r = 4%, d = 0%, T = 3 months. a) P20 = $4.95, P18 = $2.90. Is there a possible arbitrage? If so, what is your proposed arbitrage portfolio and what is the present value of your profit?
												a. Stike arbitrage in options is available between two options on the same underlying but of different stikes. Let us assume the current price is $ 18 and put option for $18 is $ 2.9 and for $20 it is $ 4.95. From the below table you can see with same duration and interest rate, the time value is higher. Therefore, one should buy P18 and sell P20. Intrinsic value will be $ 0.05 and interest earned during the period of 3 months at 4% will be $ 0.02.
																										intrinsic value	time value		Buy put option P18	Sell put option P20	intrinsic value after P15	total payout	Interest earned from Surplus
																								P20	4.95	2	2.95		0	4.95	-5	-0.05	Interest	4%	0.33%
																								P18	2.9	0	2.90		-2.9	0	3	0.1	duration	3
												CMP	18					2.05		0.05	Interest earned	0.02
												b) Instead of being able to buy and sell the options at the same price, assume there is a bid/ask spread. P20 = $4.85/$4.95 (bid/ask) and P18 = $2.85/2.95. Now is there a possible arbitrage? What happens to the profitability of the arbitrage portfolio from a)?
																								Due to increase in bid/ ask spread the profit due to arbitrage has gone. Now the possition will not give any profit since the intrinsic value has reduced to $1.9 Vs $ 2.0 in the previous case.
																																						intrinsic value	time value		Buy put option P18	Sell put option P20	intrinsic value after P15	total payout	Interest earned from Surplus
												P20	4.85	2	2.85	sell	0	4.85	-5	-0.15	Interest	4%	0.33%
												P18	2.95	0	2.95	buy	-2.95	0	3	0.05	duration	3
												CMP	18					1.9		-0.10	Interest earned	0.02