The Following Prices Are Available For Call And Put Options On A Stock
The following prices are available for call and put options on a stock priced at $50. The March options have 90 days remaining and the June options have 180 days remaining. The Black-Scholes model was used to obtain the prices. Calls Puts Strike March June
3.54 6.08 6.93 Use this information to answer the following questions. Assume that each transaction consists of one contract (100 options) unless otherwise indicated. consider a bull money spread using the March 45/50 calls.
Paper For Above instruction
This paper explores the construction and analysis of a bull call spread using March call options with strike prices of $45 and $50, utilizing the provided option prices derived from the Black-Scholes model. A bull call spread is a vertical spread strategy that involves buying a call option at a lower strike price and selling another at a higher strike price, designed to profit from a moderate rise in the underlying stock price while limiting potential losses. In this context, the strategy involves purchasing one March $45 call and selling one March $50 call, forming a debit spread with defined risk and reward parameters. The analysis includes calculations of the initial cost, maximum profit, maximum loss, profit at a specific stock price at expiration, and the breakeven point, providing a comprehensive understanding of the risk-return profile of this options trading strategy.
First, we determine the cost of establishing the spread. The cost equals the net premium paid, which is the price of the long call minus the price of the short call. Based on the provided data, the March $45 call costs $6.84, while the March $50 call costs $3.08. Therefore, the initial cost of the spread per contract is:
Cost
= Price of $45 call – Price of $50 call = $6.84 – $3.08 = $3.76 per share. Since each contract consists of 100 options, the total cost per contract is:
Total initial cost
= $3.76 × 100 = $376.
Next, we analyze the potential maximum profit. The profit for a bull call spread is limited to the difference between the strike prices minus the initial cost, which occurs if the stock price at expiration exceeds the higher strike ($50). The difference between strikes is:
Difference = $50 – $45 = $5 per share. The maximum profit per share is thus:
Maximum profit = $5 – $3.76 = $1.24 per share.
Correspondingly, the total maximum profit per contract is:
Total maximum profit
= $1.24 × 100 = $124.
The maximum loss occurs if the stock price remains below the lower strike ($45) at expiration, in which case both options expire worthless, and the initial premium paid is lost. Hence, the maximum loss is simply the initial cost, which is $376 per contract.
To determine the profit if the stock price at expiration is $47, we evaluate the payoff of each option at that stock price. The $45 call will be valuable since $47 > $45, and the $50 call will expire worthless because $47 < $50. The payoff of the spread at $47 is:
Payoff of $45 call = $47 – $45 = $2
Payoff of $50 call = $0
Net payoff = $2 – $0 = $2 per share.
The profit at this stock price is the net payoff minus the initial cost:
Profit = $2 – $3.76 = –$1.76 per share.
In dollar terms, the total profit is:
Total profit = –$1.76 × 100 = –$176.
Finally, to identify the breakeven point, we set the net payoff equal to the initial cost. The breakeven stock price (S) satisfies:
(S – $45) – the net premium paid ($3.76) = 0
S – $45 = $3.76
S = $45 + $3.76 = $48.76
Thus, the underlying stock must rise to approximately $48.76 for the spread to break even at expiration.
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