Call and Put Price Bounds Equation Formula Latex Code and Summary

Call and Put Price Bounds

Tags: #Financial #Economics

Equation

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

Latex Code

                                 (F^{P}_{t,T}(S) - Ke^{-r(T-t)})_{+} \le c(S_{t},K,t,T) \le F^{P}_{t,T}(S) \\
(Ke^{-r(T-t)} - F^{P}_{t,T}(S))_{+} \le p(S_{t},K,t,T) \le Ke^{-r(T-t)} \\ c(S_{t},K,t,T) \le C(S_{t},K,t,T) \le S_{t} \\
p(S_{t},K,t,T) \le P(S_{t},K,t,T) \le K

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Introduction

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

Latex Code

            (F^{P}_{t,T}(S) - Ke^{-r(T-t)})_{+} \le c(S_{t},K,t,T) \le F^{P}_{t,T}(S) \\
            (Ke^{-r(T-t)} - F^{P}_{t,T}(S))_{+} \le p(S_{t},K,t,T) \le Ke^{-r(T-t)} \\
            c(S_{t},K,t,T) \le C(S_{t},K,t,T) \le S_{t} \\
            p(S_{t},K,t,T) \le P(S_{t},K,t,T) \le K

Explanation

Latex code for the Calls and Puts Arbitrage. The following equations give the bounds on the prices of European calls and puts. Note that the lower bounds are no less than zero. We can also compare the prices of European and American options using the following inequalities.

$c(S_{t},K,t,T)$ : European Call Option Price
$p(S_{t},K,t,T)$ : European Put Option Price
$C(S_{t},K,t,T)$ : American Call Option Price
$P(S_{t},K,t,T)$ : American Put Option Price

Discussion

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Katherine Phillips

Wishing I could just snap my fingers and pass this test.

2023-01-17 00:00
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Dorothy Parker reply to Katherine Phillips

Nice~

2023-01-23 00:00:00.0
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Judith Morris

I've been dreaming of passing this exam.

2023-10-08 00:00
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Steven Harris reply to Judith Morris

Gooood Luck, Man!

2023-10-14 00:00:00.0
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Charles Rodriguez

I hope my efforts are enough to pass this exam.

2023-10-06 00:00
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Ralph Ward reply to Charles Rodriguez

Best Wishes.

2023-10-19 00:00:00.0
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