OPEC+ just decided to delay its meeting from December 1 to December 5.
This gives you time to consider buying some volatility.

You see that the 6 month oil future is trading at $68.50

You are looking at the 70 strike options right now expiring in 6 months

The price of the call option is $1.85

Interest rates are 4.25%

What is the price of the put option?

Question

OPEC+ just decided to delay its meeting from December 1 to December 5.
This gives you time to consider buying some volatility.

You see that the 6 month oil future is trading at $68.50

You are looking at the 70 strike options right now expiring in 6 months

The price of the call option is $1.85

Interest rates are 4.25%

What is the price of the put option?

BlackTom AI · Accepted Answer

Question recap: We have a European-style setup (likely) where a 6-month call option on oil with strike K = 70 costs C = 1.85, the current futures price S is 68.50, the risk-free annual rate r is 4.25%, and T = 0.5 years. The task is to determine the price of the corresponding put option using put-call parity.

Option by option analysis:

Option A: 3.35
- Why this is unlikely: Put-call parity for a non-dividend asset (here, a futures-based setup implies C + Ke^{-rT} = P + S) yields P ≈ C + Ke^{-rT} − S. With the numbers given, Ke^{-rT} is close to 70 × e^{-0.0425×0.5} ≈ 70 × e^{-0.02125} ≈ 68.53. Therefore P ≈ 1.85 + 68.53 − 68.50 ≈ 1.88. A put price of 3.35 would require a larger gap between Ke^{-rT} and S or an unusually high volatilitycontribution, which is not present in the parity formula. Thus 3.35 is not consistent with straightforward parity.

Option B: 4.04
- Why this is unlikely: Similar to A, parity pins P near 1.9 given the inputs. A price of 4.04 would imply a much larger credit to the put via Ke^{-rT} than is available from the current strike and discount factor, or a misalignment with the observed call price. Without any extra information (like dividends or discrete effects that could swing P upward), 4.04 would contradict the parity balance P ≈ 1.9.

Option C: 1.85
- Why this is unlikely: This option mirrors the current call price, which is unusual for a put in this setup unless underlying moves are extremely small or if S ≈ K and rT effects cancel out exactly. Our parity calculation shows P should be around 1.88, not exactly equal to C in general. Unless there is a special symmetry or the underlying is at-the-money with specific inputs, 1.85 is a coincidence rather than a result from the parity relationship. Hence it is not the precise parity value.

Option D: 3.32
- Why this is unlikely: 3.32 is again well above the parity-derived estimate of roughly 1.88. It would require a significantly larger present value of the strike or a larger disparity between S and Ke^{-rT} than the data support. Given C = 1.85 and S = 68.50, K = 70, r = 4.25%, T = 0.5, the parity-based result points away from 3.32.

Additional notes on the core concept:
- Put-call parity for European options on a non-dividend asset (or equivalently for futures-based setups) is P = C + Ke^{-rT} − S. This relation binds the four quantities (C, P, S, K) with r and T.
- Plugging in the numbers step by step: e^{-rT} ≈ e^{-0.0425×0.5} ≈ e^{-0.02125} ≈ 0.979, so Ke^{-rT} ≈ 70 × 0.979 ≈ 68.53. Then P ≈ 1.85 + 68.53 − 68.50 ≈ 1.88. So the parity-consistent put price should be around 1.88, which is closer to 1.85 than to the other discrete options listed.

In summary, evaluating each choice against the put-call parity calculation shows the other options diverge from the parity-implied value, while 1.85 is the closest to the parity-derived estimate (with rounding considerations).

fin_412_120258_251367 Mid-term Test 2

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