Calls and Puts with Different Strikes
Tags: #Financial #EconomicsEquation
$$K_{1} < K_{2} \\ 0 \le c(K_{1}) - c(K_{2}) \le (K_{2} - K_{1})e^{-rT} \\ 0 \le p(K_{2}) - p(K_{1}) \le (K_{2}) - K_{1})e^{-rT} \\ \frac{c(K_{1}) - c(K_{2})}{K_{2} - K_{1}} \ge \frac{c(K_{2}) - c(K_{3})}{K_{3} - K_{2}} \\ \frac{p(K_{1}) - p(K_{2})}{K_{2} - K_{1}} \le \frac{p(K_{3}) - p(K_{2})}{K_{3} - K_{2}}$$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
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.
: Call option of strike price K_{1}
: Call option of strike price K_{2}
American options, For three different options with strike prices K1 < K2 < K3:
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