Question

suppose that a European call option price c=4, spot price So=45,I=6 month, r=10% per annum, strike price k=30 and dividents D=0 use the put call parity to calculate the arbitrage possibillities when p=5 and p=2

Answer 1

Option 1 : Calculationg ofarbitrage possibility when p=5

Put-call parity

S + P = C + PV of (x)

Where:

S = Current Market Price

P = Value of put option at strike price 'x'

C = Value of call option at strike price 'x'

PV of (x) = Present value of strike price 'x'

$45 + $5 = $4 + $30 / (1+ 0.10 x 6/12)

$46 = $30/1.05

$46 ≠ $28.57

Here Put-call parity not hold so arbitrage possibility exist.

Arbitrager can buy the cheapest side and sell the other side.

Calculation of arbitrage possibility.

Here two possibility of stock price that is ≥ $30 or ≤$30.

If, on expiry ≥ $30		If, on expiry ≤ $30
Particular	Inflow	Outflow		Particular	Inflow	Outflow
Today				Today
Invest Money @ 10% for 6-Months	-	$46.00		Invest Money @ 10% for 6-Months	-	$46.00
Buy Call option	-	$4.00		Buy Call option	-	$4.00
Sell Stock from current market	$45.00	-		Sell Stock from current market	$45.00	-
Sell put Option	$5.00	-		Sell put Option	$5.00	-
Expiry				Expiry
Buy stock at 'p' Price	-	p		Buy stock at 'p' Price	-	p
Value of Put = 0 as market price ≥SP	-	-		Value of Put	-	$30-p
squre off call option	p-$30	-		Value of call=0 as market price≤SP	-	-
Invstment Matured ($46 + $46x10%x6/12)	$48.30	-		Invstment Matured ($46 + $46x10%x6/12)	$48.30	-
Total	$68.30+p	.p+$50		Total	$98.30	$80.000
So net Inflow ( Arbitrage Gain)	$18.300		So net Inflow ( Arbitrage Gain)	$18.300

(Arbitrager always have money left after today's transaction i.e. Sell stock, sell put and buy call option i.e. $45 + $5 -$4 = $46 remain with him so real arbitrager always like to invest whole remaining amount, So we take this amount)

Option 2 : Calculationg ofarbitrage possibility when p=2

Put-call parity

S + P = C + PV of (x)

Where:

S = Current Market Price

P = Value of put option at strike price 'x'

C = Value of call option at strike price 'x'

PV of (x) = Present value of strike price 'x'

$45 + $2 = $4 + $30 / (1+ 0.10 x 6/12)

$43 = $30/1.05

$43 ≠ $28.57

Here Put-call parity not hold so arbitrage possibility exist.

Arbitrager can buy the cheapest side and sell the other side.

Calculation of arbitrage possibility.

Here two possibility of stock price that is ≥ $30 or ≤$30.

If, on expiry ≥ $30		If, on expiry ≤ $30
Particular	Inflow	Outflow		Particular	Inflow	Outflow
Today				Today
Invest Money @ 10% for 6-Months	-	$43.00		Invest Money @ 10% for 6-Months	-	$43.00
Buy Call option	-	$4.00		Buy Call option	-	$4.00
Sell Stock from current market	$45.00	-		Sell Stock from current market	$45.00	-
Sell put Option	$2.00	-		Sell put Option	$2.00	-
Expiry				Expiry
Buy stock at 'p' Price	-	p		Buy stock at 'p' Price	-	p
Value of Put = 0 as market price ≥SP	-	-		Value of Put	-	$30-p
squre off call option	p-$30	-		Value of call=0 as market price≤SP	-	-
Invstment Matured ($43 + $43x10%x6/12)	$45.15	-		Invstment Matured ($43 + $43x10%x6/12)	$45.15	-
Total	$62.15+p	.p+$47		Total	$92.15	$77.000
So net Inflow ( Arbitrage Gain)	$15.150		So net Inflow ( Arbitrage Gain)	$15.150

(Arbitrager always have money left after today's transaction i.e. Sell stock, sell put and buy call option i.e. $45 + $2 -$4 = $43 remain with him so real arbitrager always like to invest whole remaining amount, So we take this amount)