# American Institute of Mathematical Sciences

September  2018, 8(3): 291-297. doi: 10.3934/naco.2018018

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

 1 Department of Mathematics, Faculty of Science, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor, Malaysia 2 Department of Mathematics, Faculty of Science, Institute for Mathematical Research, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor, Malaysia

* Corresponding author

Received  April 2017 Revised  July 2017 Published  June 2018

Fund Project: 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.

Citation: Teck Wee Ng, Siti Nur Iqmal Ibrahim. Pricing down-and-out power options with exponentially curved barrier. Numerical Algebra, Control & Optimization, 2018, 8 (3) : 291-297. doi: 10.3934/naco.2018018
##### References:

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##### References:
Down-and-Out Power Option with ECB: Different $\delta$
Down-and-Out Power Option with ECB: Different $K$
Down-and-Out Power Option with ECB: Different $B$
Price Comparisons: Power Call, Down-and-Out Power Barrier and Down-and-Out Power Option with ECB
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
 $K$ $\delta$ $B$ $DOPC^{ECB}$ 100 0.02 75 18.9037 100 0.05 75 18.7122 100 0.1 75 18.3433 100 0.2 75 17.3732
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
 $K$ $\delta$ $B$ $DOPC^{ECB}$ 100 0.02 75 18.9037 125 0.02 75 10.5658 150 0.02 75 5.6286 200 0.02 75 1.5268
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
 $K$ $\delta$ $B$ $DOPC^{ECB}$ 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
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
 $K$ $PC$ $DOPC$ $DOPC^{ECB}$ 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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