Lesson 4 of 20 · 6 min
Input two: the strike
The strike is the only input that never changes, and it sets where all the curvature happens.
The strike is unusual among the five inputs: it is fixed at listing and never moves for the life of the contract. Everything else in the model changes continuously. That makes the strike less a variable than a coordinate — it defines which contract you are pricing rather than what is happening to it.
Its effect on price is direct. A lower strike makes a call more valuable, because the right to acquire at a lower price is worth more. The same lower strike makes a put less valuable, because the right to dispose at a lower price is worth less. In the base case, calls at strikes of 95, 100, 105 and 110 are worth $6.21, $3.02, $1.17 and $0.35, while the corresponding puts are worth $0.90, $2.69, $5.82 and $9.99.
Notice how fast the call prices fall. Going from 100 to 105 removes 61 percent of the premium; going from 105 to 110 removes another 70 percent of what was left. That steepness is the model's statement about how much less likely large moves are than small ones, and it is the reason far out-of-the-money contracts are cheap in dollars and expensive in probability terms.
One more property, easy to verify from the numbers above. At every strike, the call price minus the put price equals the underlying minus the discounted strike. At the 100 strike: $3.02 − $2.69 = $0.33, and $100 − $99.67 = $0.33. This is put-call parity, and it is not an approximation — it follows from replication, so it holds regardless of any view about volatility.
Key terms
- Strike (K)
- The fixed transaction price in the contract. The only model input that does not change over time.
- Put-call parity
- The relationship call − put = underlying − discounted strike, for European options on the same strike and expiry. Enforced by replication.
- Convexity in strike
- The property that premiums fall away steeply as strikes move further from the price, reflecting the declining likelihood of large moves.
Worked example
The strike ladder, and parity holding at every rung
Base case: underlying 100, 30 days, rate 4%, volatility 25%. The discounted strike factor is 0.99672.
- Strike 95
- Call $6.21, put $0.90
- Strike 100
- Call $3.02, put $2.69
- Strike 105
- Call $1.17, put $5.82
- Strike 110
- Call $0.35, put $9.99
- Call premium lost, 100 → 105
- 61%
- Call premium lost, 105 → 110
- 70% of the remainder
Difference $5.31; 100 − 94.69 = $5.31.
Difference $0.33; 100 − 99.67 = $0.33.
Difference −$4.65; 100 − 104.66 = −$4.66.
Difference −$9.64; 100 − 109.64 = −$9.64.
Parity holds at every strike to the cent, and the premium ladder falls away far faster than the strikes rise.
Check yourself
In the base case the 100 call is $3.02 and the 100 put is $2.69, and the discounted strike is $99.67. Verify put-call parity and say what it depends on.
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Educational only. Nothing in this lesson is investment, legal or tax advice, or a recommendation to enter into any transaction. Figures are illustrative and computed from the inputs stated in the lesson.