Calls and Puts with Different Strikes Equation Formula Latex Code and Summary

Calls and Puts with Different Strikes

Tags: #Financial #Economics

Equation

$$K_{1} < K_{2} \\ 0 \le c(K_{1}) - c(K_{2}) \le (K_{2} - K_{1})e^{-rT} \\ 0 \le p(K_{2}) - p(K_{1}) \le (K_{2}) - K_{1})e^{-rT} \\ \frac{c(K_{1}) - c(K_{2})}{K_{2} - K_{1}} \ge \frac{c(K_{2}) - c(K_{3})}{K_{3} - K_{2}} \\ \frac{p(K_{1}) - p(K_{2})}{K_{2} - K_{1}} \le \frac{p(K_{3}) - p(K_{2})}{K_{3} - K_{2}}$$

Latex Code

                                 K_{1} < K_{2} \\
            0 \le c(K_{1}) - c(K_{2}) \le (K_{2} - K_{1})e^{-rT} \\
            0 \le p(K_{2}) - p(K_{1}) \le (K_{2}) - K_{1})e^{-rT} \\
            \frac{c(K_{1}) - c(K_{2})}{K_{2} - K_{1}} \ge \frac{c(K_{2}) - c(K_{3})}{K_{3} - K_{2}} \\
            \frac{p(K_{1}) - p(K_{2})}{K_{2} - K_{1}} \le \frac{p(K_{3}) - p(K_{2})}{K_{3} - K_{2}}

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Introduction

Equation

$c(S_{t}, K, t, T) - p(S_{t}, K, t, T) = F^{P}_{t,T}(S) - Ke^{-r(T-t)}$

Latex Code

            K_{1} < K_{2} \\
            0 \le c(K_{1}) - c(K_{2}) \le (K_{2} - K_{1})e^{-rT} \\
            0 \le p(K_{2}) - p(K_{1}) \le (K_{2}) - K_{1})e^{-rT} \\
            \frac{c(K_{1}) - c(K_{2})}{K_{2} - K_{1}} \ge \frac{c(K_{2}) - c(K_{3})}{K_{3} - K_{2}} \\
            \frac{p(K_{1}) - p(K_{2})}{K_{2} - K_{1}} \le \frac{p(K_{3}) - p(K_{2})}{K_{3} - K_{2}}

Explanation

Latex code for the Calls and Puts with Different Strikes. For European calls and puts, with strike prices K_{1} and K_{2}, where K_{1} < K_{2}, we know the following.

$c(K_{1})$ : Call option of strike price K_{1}
$c(K_{2})$ : Call option of strike price K_{2}

American options, For three different options with strike prices K1 < K2 < K3:

$c(K_{1})$ : Call option of strike price K_{1}
$c(K_{2})$ : Call option of strike price K_{2}

Discussion

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Robin Griffiths

My one wish right now is to pass this test.

2023-12-24 00:00
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Linda Brown reply to Robin Griffiths

Nice~

2024-01-15 00:00:00.0
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Cynthia Hall

Aiming for the stars with this test.

2024-02-28 00:00
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Raymond Sanchez reply to Cynthia Hall

Best Wishes.

2024-03-28 00:00:00.0
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Walter Kelley

Working hard in hopes of passing this test.

2023-06-12 00:00
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Matthew Taylor reply to Walter Kelley

Gooood Luck, Man!

2023-07-10 00:00:00.0
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