Question

The price of a call option with a strike of $100 is $10. The price of a put option with a strike of $100 is $5. Interest rates are 0 and the current price of the underlying is $100. Can you make an arbitrage profit? If so how? Describe the trade and your pay offs in detail.

Part 2: The price of a call option with a strike of $100 is $10. The price of a put option with a strike of $100 is $15. Interest rates are 0 and the current price of the underlying is $105. Can you make an arbitrage profit? If so how? Describe the trade and your pay offs in detail.

Answer 1

Put Call parity theorem shows the relationship between Call price and Put price if strike price and maturity is same for both option. If Put Call parity does not hold good then arbitrage opportunity exists in the market.

where,

C = Call price

X = Strike Price

r = interest rate (risk free)

t = maturity

S0 = current price of underlying stock

P = Put price.

Part-1

Putting the values:

Put call parity does not hold good here thus, arbitrage opportunity exist here.

Arbitrage strategy:

Call option is overvalued and Put option is under valued Thus,

Currently,

• Borrow money($95) at risk free rate and Sell Call($10)
• Buy Put($5) and Stock at Current Price($100)

On maturity,

If Stock Price > $100

1. Sell the Stock to Call buyer at $100
2. Repay the borrowed money $95 (interest rate = 0%)

Arbitrage Profit = $100 - $95 = $5

If Stock Price < $100

1. Sell the Stock to Put writer(seller) at $100
2. Repay the borrowed money $95 (interest rate = 0%)

Arbitrage Profit = $100 - $95 = $5

Part -B

Put call parity does not hold good here thus, arbitrage opportunity exist here.

Arbitrage strategy:

Put option is overvalued and Call option is undervalued Thus,

Currently,

1. Sell Stock ($105) at current price and sell Put option($15)
2. Buy call option ($10) and invest money ($110) at risk free rate

On maturity,

If Stock Price > $100

1. Withdraw invested money $110
2. Buy the Stock from Call writer at $100

Arbitrage Profit = $110 - $100 = $10

If Stock Price < $100

1. Withdraw invested money $110
2. Buy the stock from Put option holder at $100

Arbitrage Profit = $110 - $100 = $10