Question
In: Finance
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 | ||||||
Please rate the answer maximum if you get the answer and satisfied. If you remains any doubts on this answer, please leave a comment and it will be cleared.
Thank you,…
jeff jeffy answered 2 years agoRelated Solutions
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