# Analyzing the Impact of S&P Volatility Shift on ATM Straddle Sale: Calculating Loss/Gain[black scholes]

Black scholes:The 1-month implied volatility of S& ;P is 16. The slope of the skewness curve is -1 point per 1%; For example, the 99% exercise trades at a premium of 1 vol point. regarding the exercise of 100%.

You sell the ATM to straddle. It has 20 bp of vega

S& ;P rises 1%. The new at-the-money implied volatility is 15.5; The entire floating strike vol curve to expiration fell 0.5 points.

What is your loss or gain? ps:the hypothesis doesnt mean it is right please fix my wring answer

*hypotesis:
To calculate the profit or loss, we must first calculate the change in the option price due to the change in implied volatility.

The option has a vega of 20 bps, meaning that a 1 point change in implied volatility will result in a 20 bp change in the option price.

The implied volatility has decreased by 0.5 points, which means that the option price has decreased by 10 bps (20 bps x 0.5).

Since the option is a straddle, it will also be affected by the change in the price of the underlying. The S&P 500 is up 1%, meaning the option price has increased by 100 bps (since the straddle is at-the-money).

Therefore, the total profit is 90 bps (100 bps increase in option price - 10 bps decrease in option price due to the change in implied volatility).pd:also i think is related to risk-management but i couldnt ad the tag
edit:Suppose the option price before the change in the underlying price and implied volatility was $100. After the change in the price of the underlying, the option price increased by 100 bps, which means the new option price is$101.

However, due to the decrease in implied volatility, the option price decreased by 10 bps, meaning the final option price is $100.90. Therefore, the total profit is$0.90 (90 bps in percentage terms).*


please if its wrong fix it

edit: there's a small mistake in the final step. Let's go through it again:

Change in Implied Volatility:

Initial Implied Volatility (IV1) = 16 New Implied Volatility (IV2) = 15.5 Change in Implied Volatility = IV2 - IV1 = 15.5 - 16 = -0.5 The option has a vega of 20 bps, which means a 1 point change in implied volatility results in a 20 bp change in the option price. So, a 0.5 point change leads to a 10 bp change.

The option price decreases by 10 bps due to the change in implied volatility.

Change in Underlying Price:

Initial Price of Underlying (P1) = 100% S&P rises by 1%, so New Price of Underlying (P2) = 101% Since the option is a straddle at-the-money, it will be affected by the change in the price of the underlying. The option price increases by 100 bps (1%).

Total Change in Option Price:

Change in Option Price = Change due to IV + Change due to Underlying Price Change in Option Price = -10 bps (due to IV change) + 100 bps (due to underlying price change) = 90 bps This means the option price increased by 90 bps.

If the initial option price was $100, it would now be: Initial Option Price =$100

Change in Option Price = 90 bps = 0.9%

Final Option Price = $$100 + 0.9% of$$100 = \$100.90

Therefore, your total profit is $$0.90 (or 90 bps in percentage terms), assuming the initial option price was$$100.

SECOND TRY: Change in option price due to change in implied volatility:

Vega: 20 bps Change in implied volatility: -0.5 points Change in option price: Vega * Change in implied volatility = 20 bps * -0.5 points = -10 bps Change in option price due to change in underlying price:

Delta: 0.5 Change in underlying price: 1% Change in option price: Delta * Change in underlying price = 0.5 * 1% = 0.5% Total change in option price:

Change in option price due to change in implied volatility: -10 bps Change in option price due to change in underlying price: 0.5% Total change in option price: -10 bps + 0.5% = 0.4% Conclusion:

The net change in option price is 0.4%, which is very small. Therefore, the trader can expect to make no significant profit or loss on this trade.

Note:

The delta of a straddle is not exactly 0.5, but it is close. For the sake of simplicity, we assumed a delta of 0.5 in our calculation.

Blockquote


Calculate the change in option price due to the change in implied volatility. Formula: Vega * Change in implied volatility

Vega: 20 bps Change in implied volatility: -0.5 points

Change in option price due to change in implied volatility = 20 bps * -0.5 points = -10 bps

Calculate the change in option price due to the change in underlying price. Formula: Delta * Change in underlying price

Delta: 0.5 Change in underlying price: 1%

Change in option price due to change in underlying price = 0.5 * 1% = 0.5%

Calculate the total change in option price. Formula: Change in option price due to change in implied volatility + Change in option price due to change in underlying price

Total change in option price = -10 bps + 0.5% = 0.4%

Conclusion:

The net change in option price is 0.4%, which is very small. Therefore, the trader can expect to make no significant profit or loss on this trade.

thanks.

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Oct 27, 2023 at 6:11