European put option pricing analysis
Cost of european put - 1.5 years out. 33K strike, current 24.4K, risl free rate 6.5, vol = 15%
about 14 hours ago
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I'll calculate the price of this European put option using the Black-Scholes formula.## European Put Option — Black-Scholes Pricing
| Parameter | Value |
|---|---|
| Spot (S) | 24,400 |
| Strike (K) | 33,000 |
| Time to Expiry (T) | 1.5 years |
| Risk-Free Rate (r) | 6.50% |
| Volatility (σ) | 15.0% |
| d₁ | –1.020890 |
| d₂ | –1.204602 |
| N(–d₁) | 0.8463 |
| N(–d₂) | 0.8858 |
| Put Price | 5,865.65 |
This put is deep in-the-money (strike 33,000 vs spot 24,400, giving ~8,600 of intrinsic value). At 15% vol with 1.5 years to expiry, the put prices at 5,865.65. The time value component is small given the deep ITM nature — the bulk of the premium reflects intrinsic value discounted by the risk-free rate.
about 14 hours ago
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And call price?
about 14 hours ago
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European Call Option — Black-Scholes
| Parameter | Value |
|---|---|
| Spot (S) | 24,400 |
| Strike (K) | 33,000 |
| Time to Expiry (T) | 1.5 years |
| Risk-Free Rate (r) | 6.50% |
| Volatility (σ) | 15.0% |
| d₁ | –1.020890 |
| d₂ | –1.204602 |
| N(d₁) | 0.1537 |
| N(d₂) | 0.1142 |
| Call Price | 331.28 |
Summary:
| Price | |
|---|---|
| Put | 5,865.65 |
| Call | 331.28 |
The call is deep out-of-the-money (strike 33,000 vs spot 24,400). With only a ~15% probability of finishing ITM at these levels, the call prices at just 331.28. The ~8,600 gap between the two reflects the deep intrinsic value captured by the put — consistent with put-call parity (C – P = S – Ke⁻ʳᵀ).
about 14 hours ago