Financial
Option Put-Call Parity, Intrinsic Value, and Time Value formulas
Use a no-dividend European option parity model to infer a put value, then calculate the sample call premium minus intrinsic value.
European put-call parity under explicit assumptions
For European call and put options with the same underlying, strike and expiry, no dividends, a continuously compounded financing rate and frictionless no-arbitrage assumptions, C - P = S - K * EXP(-r*T). A quoted call price supplies C; parity infers P under those assumptions, rather than forecasting a traded price.
Call intrinsic value is MAX(0,S-K); put intrinsic value is MAX(0,K-S). Premium minus intrinsic is often called time or extrinsic value. It need not be nonnegative for every European option because immediate exercise is unavailable. Here the sample call difference is 4.20. This subtraction is not an estimate of volatility alone.
| Option Metric (S=$105, K=$100, r=5%, T=0.5y, C=$9.20) | Formula | Result |
|---|---|---|
| PV of Strike K * EXP(-r*T) | 100 * EXP(-0.05 * 0.5) | $97.53 |
| Parity-implied put value under the model | 9.20 - 105 + 97.53099 | $1.73 |
| Call Intrinsic vs. Time Value | MAX(0, 105-100) = $5.00 | Time Value = $9.20 - $5.00 = $4.20 |
Implied European Put price from Put-Call Parity
A2=Spot (105), B2=Strike (100), C2=Rate (0.05), D2=Years (0.5), E2=Call Price (9.20).
=IF(OR(COUNT(A2:E2)<>5,A2<=0,B2<=0,D2<0,E2<0),"Invalid inputs",LET(putValue,E2-A2+B2*EXP(-C2*D2),IF(OR(putValue<0,E2>A2,AND(D2=0,E2<>MAX(0,A2-B2))),"Inconsistent prices",ROUND(putValue,2))))Decompose Call Intrinsic Value and Extrinsic Time Value
The formula subtracts call intrinsic value from the supplied call price. A negative result is retained for inspection; it does not automatically establish an executable arbitrage. Dividends, exercise style, bid/ask spreads, financing and quote timing require separate treatment.
=IF(OR(COUNT(A2:E2)<>5,A2<=0,B2<=0,D2<0,E2<0),"Invalid inputs",ROUND(E2 - MAX(0, A2 - B2), 2))Try the example
Use the original values or change them to test your understanding.