Stock Price is currently $120. A call on Toronto's stock price with an exercise price of $95 currently trades for $31. A put on Igloo's stock with an exercise price of $95 currently trades for $2. For simplicity, the par value of the risk-free bond is $95, the risk-free rate is 5% and the time to maturity is six months. Construct a portfolio to arbitrage the misplacing in the put-call parity.
What is the relevant risk free rate for an option expiring in 10 days, the bid discount is 4.5 and the ask discount is 4.56?
1.)Put-Call Parity = Stock + put = Call + PV of Bond.
Stock + Put = 120 + 2 =122
Call + PV of Bond = 31+ (95/ 1.05^0.5) = 31 + 92.71 = 123.71
As we've established that there is misplaced Put-Call Parity we can construct a portfolio in the following way.
We long (buy) the stock @ 120 and take a long position in Put
Option by paying $2. &
We take a short (sell) position in Bond @ 95 & Call Option
$31.
2.) Risk Free rate.
Average BId Ask Discount = (4.5+4.56)/2 = 4.53
Price = [100- 4.53(10/365)] = 99.87589.
Risk Free return = 100/Price ^ 365/10-1
Risk Free Rate = 4.637 %
Stock Price is currently $120. A call on Toronto's stock price with an exercise price of...