The Following Quotes Were Observed For Options On A Given St

The Following Quotes Were Observed For Options On A Given Stock On Nov

The assignment involves analyzing various options scenarios based on given quote data for options on a specific stock observed on November 1. The tasks include determining the conditions under which specific options make a profit or are exercised, calculating intrinsic and time values of options, and evaluating strategies such as spreads and straddles. Additionally, the assignment requires examining payoffs and profits for different option positions, including buying calls, puts, and constructing complex strategies like covered calls and strips. The analysis involves applying fundamental concepts of options trading, such as intrinsic value, time value, profit-loss calculations, and understanding exercise conditions.

Paper For Above instruction

Options trading involves a comprehensive understanding of the conditions under which options are profitable and how different strategies can be implemented based on market scenarios. This paper delves into the analysis of options quotes for a specific stock observed on November 1, examining various scenarios of exercising options, calculating their intrinsic and time values, and analyzing strategic positions like spreads and straddles, as well as the implications of market movements on profits and losses.

Analyzing Exercise Conditions and Profitability of Options

Options give traders the right, but not the obligation, to buy or sell an underlying asset at a specified strike price before or at expiration. The profitability of holding or exercising an option depends on the relationship between the stock's market price at expiration and the option's strike price, alongside premiums paid. For instance, the holder of a call option profits when the stock's market price exceeds the strike price by more than the premium paid; similarly, a put option holder profits when the stock price falls below the strike price by more than the premium. These fundamental principles underpin the analysis of specific options scenarios discussed here.

Question a: Conditions for the January 110 Call to Make a Gain

The January 110 call gives the holder the right to purchase the stock at $110. To realize a gain, the stock price must exceed the strike price plus the premium paid ($8.30). From the quote, the premium is $8.30. Therefore, at expiration, the stock price must be greater than:

$110 + $8.30 = $118.30

Thus, the holder will achieve a profit if the stock closes above $118.30 at expiration, considering transaction costs are ignored. If the stock price remains below this threshold, the option expires worthless or incurs a loss, depending on how close the price is to the strike plus premium.

Question b: Conditions for the November 115 Put to Make a Gain

The November 115 put gives the holder the right to sell at $115. The premium paid for this put is $5.30. To profit, the stock price must be below the strike minus the premium:

$115 - $5.30 = $109.70

If the stock decreases below $109.70 at expiration, exercising the put yields a profit after accounting for the premium paid; otherwise, the option expires worthless or results in a loss.

Question c: Conditions for the December 105 Call to Make a $200 Gain

The December 105 call premium is $2.50. Each standard options contract typically covers 100 shares. The profit of $200 corresponds to a net gain after considering premium costs and underlying stock price at expiration. The profit from exercising this call is determined by:

(Stock Price at expiration - Strike Price) x 100 - Premium Paid x 100 = $200

Let x be the stock price at expiration:

(x - 105) x 100 - 2.50 x 100 = 200

Simplify:

100x - 10,500 - 250 = 200

100x = 10,700

x = 107

Since the stock price must be above the strike price for the call to be profitable, and considering the premium paid, the minimum stock price at expiration to realize a $200 profit is $107. At this price, the intrinsic value per share is $2, so total profit per contract is $200 when profit is netted after premiums.

Question d: When Will the December 105 Call Be Exercised?

The December 105 call will be exercised when the stock price exceeds the strike price ($105) by more than the premium paid ($2.50). Practically, if at expiration, the stock trades above $105 + $2.50 = $107.50, the holder benefits from exercising the call to buy shares at $105 and potentially selling them at the market price, realizing a profit. If the stock remains below $107.50, exercising the call would be unprofitable, so it remains unexercised.

Question e: When Will the November 110 Put Be Obligated to Be Exercised?

The holder of a put option is obligated to exercise if it is profitable to do so. The November 110 put provides the right to sell at $110, with the premium paid not specified here but assumed from context. The put would be exercised if, at expiration, the stock price falls below the strike price minus the premium, effectively when the option is in the money. If the stock price drops significantly below $110, exercising becomes profitable to sell shares at $110, regardless of the premium cost, since the intrinsic value is > 0. The put would be exercised if the stock price falls below $110, ensuring the holder can sell at the higher strike price for profit.

Analyzing Option Pricing and Strategies Using the Black-Scholes Model

The second set of data involves options prices for a stock priced at $50, utilizing the Black-Scholes model for valuation. Key aspects include calculating intrinsic and time values, and constructing options strategies such as spreads and straddles to profit from expected market moves.

Question 1: Intrinsic Value of June 55 Put

The intrinsic value of a put is max(0, strike price - underlying asset price). For the June 55 put:

55 - 50 = 5

Since the stock is at $50 and the strike is 55, the put's intrinsic value is $5 per share. For one contract of 100 options, total intrinsic value equals $5 x 100 = $500.

Question 2: Intrinsic Value of March 55 Call

The call's intrinsic value is max(0, stock price - strike price). Here:

50 - 55 = -5, which is less than zero, so the call has no intrinsic value; it is out of the money. Therefore, intrinsic value is $0.

Question 3: Time Value of June 50 Put

The time value = option price - intrinsic value. The June 50 put price is $6.93; intrinsic value at $50 stock price is zero (since strike equals stock price). Therefore, time value = $6.93.

Question 4: Time Value of March 45 Call

Price of March 45 call = $2.89, and intrinsic value = max(0, 50 - 45) = $5. Since the call's market price ($2.89) is less than the intrinsic value, which indicates an arbitrage opportunity, however, generally, the total observed price accounts for time value and implied volatility. Assuming no arbitrage, the market price is less than intrinsic value, indicating the call is out-of-the-money, so the actual intrinsic value is

Question 5a: Cost of a Bull Money Spread with March 45/50 Calls

The bull spread involves buying the March 45 call and selling the March 50 call. The cost is the net premium paid:

Price of March 45 call = $2.89, Price of March 50 call = $4.89

Cost = $2.89 - $4.89 = -$2.00 (a net debit of $2 per share, or $200 per contract).

Question 5b: Maximum Profit on the Spread

The maximum profit occurs when the stock price exceeds the higher strike (50), enabling both options to be exercised optimally. Profit equals the difference between strikes minus net premium paid:

(50 - 45) - (Cost) = 5 - 2 = $3 per share, or $300 per contract.

Question 5c: Maximum Loss on the Spread

The maximum loss is limited to premium paid when stock remains below the lower strike (45), and the options expire worthless:

Net premium paid = $2, so maximum loss is $200 per contract.

Question 5d: Profit if Stock Price at Expiration is $47

At $47, the March 45 call is in the money with intrinsic value ($47 - $45) = $2, and the March 50 call is out of the money. The profit per share is:

Intrinsic value of bought call = $2, minus net premium paid ($2), resulting in breakeven, so zero profit. Including transaction costs, no profit or loss occurs.

Question 6a: Cost of Long Straddle with June 50 Options

The cost of the straddle = price of the June 50 call + price of the June 50 put:

$6.93 + $6.84 = $13.77 per share, or $1,377 per contract.

Question 6b: Breakeven Stock Prices at Expiration

Upper breakeven = strike + total cost: 50 + 13.77 = $63.77

Lower breakeven = strike - total cost: 50 - 13.77 = $36.23

Question 6c: Profit if Stock Price at Expiration is $64.75

Since the stock exceeds the upper breakeven, the profit is:

($64.75 - 50) - 13.77 = 14.75 - 13.77 = $0.98 per share, or $98 per contract.

Question 6d: Adding a Put to Form a Strip and Calculating Profit at $36

A strip involves one call and two puts. Assuming units are 100 options each, the total initial cost is:

Cost of call = $6.84, cost of two puts = 2 x $4.89 = $9.78, total = $16.62 per share.

At expiry, stock price = $36, the call's intrinsic value = $0 (out of money), puts' intrinsic value each = ($55 strike - $36) = $19, total for two puts = 2 x $19 = $38.

Net profit = intrinsic value of puts - total cost = 38 - 16.62 = $21.38 per share, or $2,138 per contract.

Analyzing a European Stock and Options Positioning

Consider a stock priced at $30, with European call and put options at the same strike of $30 and expiration in six months. The call costs $2.89, and the put costs $2.15. The analysis involves examining profits from different strategies and market movements.

Question 1: Buying a Call at Expiration with Stock at $37

The intrinsic value of the call is ($37 - 30) = $7 per share. Profit per share = intrinsic value - premium paid = 7 - 2.89 = $4.11. Total profit for 100 options = $411.

Question 1b: Breakeven Stock Price at Expiration

Breakeven = strike + premium of call = $30 + $2.89 = $32.89.

Question 1c: Maximum Profit from Buying the Call

The maximum profit is theoretically unlimited as the stock price can rise indefinitely. Practically, it is the difference between stock price and strike minus premium paid as the stock price increases beyond breakeven.

Question 1d: Maximum Profit for the Call Writer

The writer's maximum profit occurs if the stock price remains below $30 at expiration, with the option expiring worthless, earning the amount of premium received, i.e., $2.89 per share or $289 per contract.

Question 2a and 2b: Constructing a Covered Call with Stock at $27 and $41

At $27, the stock's value is below the strike; the profit comprises the premium received plus any stock appreciation (if held), minus the cost of the option. At $27, the call expires worthless, so profit = stock's lower value plus premium - initial stock cost (if the stock was owned). At $41, the call is in the money with intrinsic value ($41 - $30) = $11; thus, profit includes the premium ($2.89) plus stock appreciation minus the strike price. The exact profit depends on initial purchase price; assuming initial cost at $30, profit at $41 = ($11 + $2.89) - ($30) = $13.89.

In conclusion, options and strategies are best employed based on market outlooks, and understanding the intrinsic and time values aids in making profitable decisions across scenarios.

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