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The current price of a piece of Gold jewelry is $1380. The annual risk free rate...

The current price of a piece of Gold jewelry is $1380. The annual risk free rate is 3 percent. A put option on the jewelry with an exercise price of $1390 and one year until expiration has a current value of $19.25. A call option on the jewelry with an exercise price of $1390 has a current value of $21.35 is there an arbitrage opportunity? If yes, what is the value of the arbitrage? Explain exactly how exploit the arbitrage

Solutions

Expert Solution

According to Put call parity = (Spot price + put premium) = (((Strike priceX e^-(rt)) + call premium)
put premium = (((Strike priceX e^-(rt)) + call premium) - Spot price
e^-(rt) = e-^(0.03X1) = e ^-0.03 = 0.970445501203472
(Strike priceX e^-(rt)) =1390 X 0.970445501203472 1348.919247
put premium = 1348.91924667283 + 21.35 - 1380 = 12.8411890903007
Put premium rounded = $12.84
Spot price = current price = $1380,
r =The annual risk free rate is 3 percent,
exercise price of $1390,
put option premium = $19.25
call option has a current value of $21.35
t =one year
call premium = (Spot price + put premium) - (((Strike priceX e^-(rt))
Call premium = 1380+ 19.25 -1348.91924667283 =50.33075332717
Theoritical price is more than actual price, so buy call at the same time sell (write)put and sell jewellary in spot
then we will get $1380 in spot and $19.25 for put option so total inflow = $1399.25
and buy Call at $21.35, then net balance = 1399.25-21.35 =1377.90
and invest this for 1 year, then we will get = 1377.9 X e^rt = 1377.9X 1.03045456829866 = 1419.8633496587
When gold jewellary price goes above $1390, we will exercise call option, then we will get back our share At $1390
our gain will be $1419.86334965872 - 1390 = $29.8633496587199
When gold jewellary price goes below $1390, the buyer of put option will exercise his option and will give the share and
optain $1390. Then also we will get back our share At $1390
our gain will be $1419.86334965872 - 1390 = $29.8633496587199

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