Question

Part A.

True or False?

“Long Straddle generates large losses when the underlying stock price decreases significantly.”

Discuss your original answer with example.

Part B.

True or False?

“According to the Risk-Neutral Valuation, the option price should be determined using probabilities in the actual world.”

Discuss your original answer with example.

Answer 1

Part A.

“Long Straddle generates large losses when the underlying stock price decreases significantly.”

This statement is false

A straddle strategy can be used to exploit the market condition in any direction where one call option and one put option of a stock with same strike price and same expiry date are purchased.

Long straddle will make the profit either at above the stock price = stock price - strike price + (Put price + call price)

Or at below the stock price = strike price + (Put price + call price) – stock price

And,

Total cost of straddle = Call price +Put price

Therefore loss is limited to the cost of straddle.

Example:

Assume that Strike price is $80, if stock price is below or at $80, call payoff will be zero and if stock price is above or at $80, put payoff will be zero.

Put price = $2.40

Call price = $ 4.50

Stock price	Call payoff	Put Payoff	Total Payoff (call payoff +put payoff)	Total profit [total payoff – (put price +call price)]
$70	$0 (Its below $80)	$80 -$70 =$10	$10	$10-($2.40+$4.50)=$3.10
$75	$0 (Its below $80)	$80 -$75 = $5	$5	$5-($2.40+$4.50) = -$1.90
$80	$0 (It’s at $80)	$0 (it’s at $80)	$0	$0 -($2.40+$4.50) =-$6.90
$85	$85 -$80 =$5	$0 (its above $80)	$5	$5 -($2.40+$4.50) =-$1.90
$90	$90 -$80 =$10	$0(its above $80)	$10	$10-($2.40+$4.50) =$3.10

Part B.

“According to the Risk-Neutral Valuation, the option price should be determined using probabilities in the actual world.”

This statement is false

Theoretical probabilities are used in Risk-Neutral Valuation. If real-world probabilities are used in Risk-Neutral Valuation then expected values of options are required to be adjusted for its individual risk profile.

Example:

We can use risk neutral probability to find out the value of call option

Risk neutral probability move up for one period

P = (R-D)/ (U-D)

Where, R = 1+r (r is risk free rate)

Assume that R = 1+10% = 1.10

Chances of moving up the stock after one period, U = 130/100 = 1.30

Chances of moving down the stock after one period, D = 90/100 = 0.9

Therefore

Risk neutral probability P = (1.10 -0.90)/ (1.30 - 0.90) =0.50

Risk neutral probability to move down

q = 1 –p = 1- 0.5 = 0.50