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Article Contents

# Pricing down-and-out power options with exponentially curved barrier

• * Corresponding author

The first author is supported by Universiti Putra Malaysia and the Fundamental Research Grant Scheme

• Power barrier options are options where the payoff depends on an underlying asset raised to a constant number. The barrier determines whether the option is knocked in or knocked out of existence when the underlying asset hits the prescribed barrier level, or not. This paper derives the analytical solution of the power options with an exponentially curved barrier by utilizing the reflection principle and the change of measure. Numerical results show that prices of power options with exponentially curved barrier are cheaper than those of power barrier options and power options.

Mathematics Subject Classification: Primary: 91G30, 91G60, 91G80; Secondary: 62P05.

 Citation:

• Figure 1.  Down-and-Out Power Option with ECB: Different $\delta$

Figure 2.  Down-and-Out Power Option with ECB: Different $K$

Figure 3.  Down-and-Out Power Option with ECB: Different $B$

Figure 4.  Price Comparisons: Power Call, Down-and-Out Power Barrier and Down-and-Out Power Option with ECB

Table 1.  Prices of DOPC with ECB with different curvature, $\delta$

 $K$ $\delta$ $B$ $DOPC^{ECB}$ 100 0.02 75 18.9037 100 0.05 75 18.7122 100 0.1 75 18.3433 100 0.2 75 17.3732

Table 2.  Prices of DOPC with ECB with different strike price, $K$

 $K$ $\delta$ $B$ $DOPC^{ECB}$ 100 0.02 75 18.9037 125 0.02 75 10.5658 150 0.02 75 5.6286 200 0.02 75 1.5268

Table 3.  Prices of DOPC with ECB with different barrier level, $B$

 $K$ $\delta$ $B$ $DOPC^{ECB}$ 100 0.02 55 20.5649 100 0.02 65 20.3056 100 0.02 75 18.9037 100 0.02 85 14.6799 100 0.02 90 10.9949 100 0.02 95 6.1064

Table 4.  Price Comparisons$:$ Power Call, Down-and-Out Power Barrier, and Down-and-Out Power Option with ECB

 $K$ $PC$ $DOPC$ $DOPC^{ECB}$ 100 20.5851 19.0205 18.9037 125 11.0876 10.6020 10.5658 150 5.7955 5.6402 5.6286 200 1.5459 1.5279 1.5268 250 0.4213 0.4195 0.4194
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