It is the days after the Supreme Court rules tariffs are illegal. Markets are rallying.

SPX = 6000

K = 5900

t = 3 months (0.25)

r = 4.5%

Implied Volatility = 25%

You bought a put before the news when the SPX was 5900 at a price of 265. The price of the put is now 225.

The delta of the option is:

Question

It is the days after the Supreme Court rules tariffs are illegal. Markets are rallying.

SPX = 6000

K  = 5900

t = 3 months (0.25)

r = 4.5%

Implied Volatility = 25%

You bought a put before the news when the SPX was 5900 at a price of 265. The price of the put is now 225.

The delta of the option is:

BlackTom AI · Accepted Answer

We need to restate the scenario and evaluate how the put option's price responds to moves in the underlying index.
- The underlying SPX moved from 5900 (when the put was bought) to 6000 (current), a rise of 100 points.
- The put's price changed from 265 to 225, a drop of 40.
- Delta measures the sensitivity of the option price to a 1-point change in the underlying: dP ≈ Delta × dS.
- For a put option, Delta is negative, so the magnitude |Delta| tells us how many dollars the put price changes per 1-point move in SPX.

Option 1: 20
- If Delta magnitude were 0.20, a 100-point rise in SPX would change the put price by about 0.20 × 100 = 20, but the observed drop is 40, which is not consistent with |Delta| = 0.20.
- Additionally, put Delta for this scenario would be larger in magnitude given the money and time remaining, so 0.20 is too small.

Option 2: 30
- A Delta magnitude of 0.30 would imply a 100-point move changes the put price by about 30, which still does not match the observed 40 change.
- This underestimates the actual sensitivity in this setup.

Option 3: 50
- If |Delta| were 0.50, the price change would be around 50 for a 100-point move, which overshoots the observed 40 decrease.
- This would imply a stronger sensitivity than what occurred.

Option 4: 40
- With |Delta| ≈ 0.40, a 100-point increase in SPX would produce a price change of about 40 in the put (0.40 × 100 = 40).
- Since the observed price drop is 40 when SPX rises by 100, this aligns well with the approximate delta magnitude for a put with K = 5900, SPX around 6000, and the given parameters.
- Note on sign: put Delta is negative, so the direction is consistent (SPX up → put price down). Here we report the magnitude 40, which matches the observed absolute change.

fin_412_120258_251367 Mid-term Test 2

It is the days after the Supreme Court rules tariffs are illegal. Markets are rallying. SPX = 6000 K = 5900 t = 3 months (0.25) r = 4.5% Implied Volatility = 25% You bought a put before the news when the SPX was 5900 at a price of 265. The price of the put is now 225. The delta of the option is:

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