Research Article
Proactive Hedging European Option Pricing with a General Logarithmic Position Strategy
Table 2
Price ratios of exotic options considering the proactive hedging options relative to classical European options in terms of
, , , , and
parameters.
| | Strategy parameters | Price ratios of exotic options with classical option | | | | | | | | Logarithmic | Linear | Logarithmic | Linear | Logarithmic | Linear |
| | 0.5 | 0.3 | 0.6 | 0 | 0.60 | 0.61 | 0.63 | 0.64 | 0.66 | 0.67 | | 0.5 | 0.3 | 0.6 | 7 | 0.97 | 0.97 | 0.99 | 0.99 | 1.00 | 1.00 | | 0.5 | 0.3 | 0.6 | 15 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | 0.5 | 0.5 | 0.6 | 0 | 0.47 | 0.47 | 0.48 | 0.48 | 0.49 | 0.49 | | 0.5 | 0.5 | 0.6 | 7 | 0.96 | 0.96 | 0.99 | 0.99 | 1.00 | 1.00 | | 0.5 | 0.5 | 0.6 | 15 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | 0.5 | 0.5 | 1 | 0 | 0.34 | 0.36 | 0.39 | 0.40 | 0.44 | 0.45 | | 0.5 | 0.5 | 1 | 7 | 0.95 | 0.95 | 0.99 | 0.99 | 1.00 | 1.00 | | 0.5 | 0.5 | 1 | 15 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | 0.7 | 0.3 | 0.6 | 0 | 0.63 | 0.64 | 0.65 | 0.66 | 0.67 | 0.68 | | 0.7 | 0.3 | 0.6 | 7 | 0.97 | 0.97 | 0.99 | 0.99 | 1.00 | 1.00 | | 0.7 | 0.3 | 0.6 | 15 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | 0.7 | 0.5 | 0.6 | 0 | 0.48 | 0.48 | 0.48 | 0.49 | 0.49 | 0.49 | | 0.7 | 0.5 | 0.6 | 7 | 0.96 | 0.96 | 0.99 | 0.99 | 1.00 | 1.00 | | 0.7 | 0.5 | 0.6 | 15 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | 0.7 | 0.5 | 1 | 0 | 0.38 | 0.40 | 0.41 | 0.43 | 0.45 | 0.46 | | 0.7 | 0.5 | 1 | 7 | 0.95 | 0.95 | 0.99 | 0.99 | 1.00 | 1.00 | | 0.7 | 0.5 | 1 | 15 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | 1 | 0.3 | 0.6 | 0 | 0.64 | 0.66 | 0.66 | 0.67 | 0.68 | 0.68 | | 1 | 0.3 | 0.6 | 7 | 0.97 | 0.97 | 0.99 | 0.99 | 1.00 | 1.00 | | 1 | 0.3 | 0.6 | 15 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | 1 | 0.5 | 0.6 | 0 | 0.48 | 0.49 | 0.49 | 0.49 | 0.49 | 0.50 | | 1 | 0.5 | 0.6 | 7 | 0.96 | 0.96 | 0.99 | 0.99 | 1.00 | 1.00 | | 1 | 0.5 | 0.6 | 15 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | 1 | 0.5 | 1 | 0 | 0.41 | 0.43 | 0.43 | 0.45 | 0.46 | 0.47 | | 1 | 0.5 | 1 | 7 | 0.95 | 0.95 | 0.99 | 0.99 | 1.00 | 1.00 | | 1 | 0.5 | 1 | 15 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
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