Question

In: Finance

The following options are available: 3-month European call with a strike price of $20 that is priced at $1.00

 

The following options are available:

3-month European call with a strike price of $20 that is priced at $1.00

3-month European put with a strike price of $20 that is priced at $4.00

3-month call with a strike price of $25 that is priced at $8.50

3-month put with a strike price of $25 that is priced at $7.00

Currently, the price of the underlying stock is $25.50

1)Identify all arbitrage trades, not considering interest.

2)For each set of trades you will make, please describe the trades you do and how much money you will make.

Then, go back to each set or trades and state if you will make “more” or “less” if you were to consider interest.

Solutions

Expert Solution

1)

Arbitrage Trades

Buying Call options

3-month European call with a strike price of $20 that is priced at $1.00

Currently, the price of the underlying stock is $25.50

 = $25.50-($20+$1.00)

 = $4.5

 

2)

For each set of trades you will make, please describe the trades you do and how much money you will make.

3-month European call with a strike price of $20 that is priced at $1.00

Currently, the price of the underlying stock is $25.50

 = Stock Price - Strike Price

 = $25.50-($20+$1.00)

 = $4.5

 

3-month European put with a strike price of $20 that is priced at $4.00

Currently, the price of the underlying stock is $25.50

 = Strike Price - Stock price

 = $20- $25.50

 = 0

 

The PUT option is worthless

 

3-month call with a strike price of $25 that is priced at $8.50

Currently, the price of the underlying stock is $25.50

 = Stock - (Strike Price + Premium )

 = $25.50 - ($25+ $8.50)

 = -$8.0

 

3-month put with a strike price of $25 that is priced at $7.00

Currently, the price of the underlying stock is $25.50

 = Strike - Stock

 = $25 - $25.50

 = 0

(Option is worthless)

 

If we factor in interest rate let's say 4% for the profit-making options

 

3-month European call with a strike price of $20 that is priced at $1.00

Currently, the price of the underlying stock is $25.50

 = Stock Price - Strike Price /(1+4%*3/12)

 = $25.50-($20+$1.00)

 = $25.50- ($19.80+$1.00)

 = $4.70

 

By factoring in the interest rate and the present value of the strike price, we will make more profit.

Previous profit i.e.$4.50 < $4.70.

1) Arbitrage Trades is $4.5.

 

Junaid answered 2 years ago
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