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Assume you have the following 3 month options (and their premiums) on XYZ available, where So = $52.00: Call, K=$50.00, premium=$5.00 Call, K=$52.00, premium=$4.00 Call, K=$54.00, premium=$3.00 Put, K=$50.00, premium=$3.00 Put, K=$52.00, premium=$4.00 Put, K=$54.00, premium=$5.00 You construct a short $50.00/$52.00 strangle. If the underlying price at expiry is $60.00, what is the gain/loss on your strategy? (Note: Please show a loss as a negative number)

Question

Assume you have the following 3 month options (and their premiums) on XYZ available, where So = 52.00:Call,K=52.00: Call, K=50.00, premium=5.00Call,K=5.00 Call, K=52.00, premium=4.00Call,K=4.00 Call, K=54.00, premium=3.00Put,K=3.00 Put, K=50.00, premium=3.00Put,K=3.00 Put, K=52.00, premium=4.00Put,K=4.00 Put, K=54.00, premium=5.00Youconstructashort5.00 You construct a short 50.00/52.00strangle.Iftheunderlyingpriceatexpiryis52.00 strangle. If the underlying price at expiry is 60.00, what is the gain/loss on your strategy? (Note: Please show a loss as a negative number)

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Solution

A short strangle strategy involves selling a call and a put option on the same underlying asset with the same expiry date but with different strike prices. In this case, you are selling a call option with a strike price of 52.00andaputoptionwithastrikepriceof52.00 and a put option with a strike price of 50.00.

The premium received from selling these options is the income from this strategy. The premium received from selling the call option is 4.00andfromtheputoptionis4.00 and from the put option is 3.00. So, the total premium received is 4.00+4.00 + 3.00 = $7.00.

At expiry, if the underlying price is 60.00,theputoptionwillexpireworthlessasthemarketpriceishigherthanthestrikeprice.However,thecalloptionwillbeexercisedasthemarketpriceishigherthanthestrikeprice.Thelossfromthecalloptionisthedifferencebetweenthemarketpriceandthestrikeprice,i.e.,60.00, the put option will expire worthless as the market price is higher than the strike price. However, the call option will be exercised as the market price is higher than the strike price. The loss from the call option is the difference between the market price and the strike price, i.e., 60.00 - 52.00=52.00 = 8.00.

So, the total loss from the strategy is the loss from the call option minus the premium received, i.e., 8.008.00 - 7.00 = $1.00.

Therefore, the loss on your strategy is 1.00.Aspertheinstruction,alossshouldbeshownasanegativenumber,sothelossis1.00. As per the instruction, a loss should be shown as a negative number, so the loss is -1.00.

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