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0 0.2 0.4 0.6 0.8 10
0.2
0.4
0.6
0.8
1
u
v
Random sample from Frank Copula
0 0.2 0.4 0.6 0.8 10
0.2
0.4
0.6
0.8
1
u
v
Random sample from Clayton Copula
0 0.2 0.4 0.6 0.8 10
0.2
0.4
0.6
0.8
1
u
v
Random Sample from Gumbel Copula
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49/85
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51/85
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0 200 400 600 800 1000 12006.5
7
7.5
8
8.5
9
9.5
10x 10
3
Observations
U S D / J P Y E x c h a n g e
R a t e
Time series plot of USD/JPY Exchange Rate
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0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90.08
0.09
0.1
0.11
0.12
0.13
Delta
V o l a t i l i t y
Market and model volatilities for USD/JPY FX options with maturity 1 month
Heston with jumps volatilityMarket volatility
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90.08
0.09
0.1
0.11
0.12
0.13
Delta
V o l a t i l i t y
Market and model volatilities for USD/JPY FX options with maturity 3 months
Heston with jumps VolatilityMarket Volatility
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62/85
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90.08
0.09
0.1
0.11
0.12
0.13
Delta
V o l a t i l i t y
Market and model volatilities for USD/JPY FX options with maturity 6 months
Heston with jumps VolatilityMarket Volatility
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90.08
0.09
0.1
0.11
0.12
0.13
Delta
V o l a t i l i t y
Market and model volatilities for USD/JPY FX options with maturity 1 year
Heston with jumps VolatilityMarket Volatility
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63/85
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90.08
0.09
0.1
0.11
0.12
0.13
Delta
V o l a t i l i t y
Market and model volatilities for USD/JPY FX options with maturity 2 years
Heston with jumps VolatilityMarket Volatility
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10 12 14 16 18 20 22 24 26 28 30232
234
236
238
240
242
244
246
248Cannonical Maximum Likelihood Estimation (Mashal and Zeevi)
Degrees of Freedom
V a
l u e o
f L o g
L i k e
l i h o o
d F u n
c t i o n
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0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90.11
0.115
0.12
0.125
0.13
0.135
Delta
V o
l a t i l i t y
Volatilities on EUR/USD FX Options for maturity of 1 month
Market VolatilityHeston with jumps Volatiltity
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90.11
0.115
0.12
0.125
0.13
0.135
Delta
V o
l a t i l i t y
Volatilities on EUR/USD FX Options for maturity of 6 months
Market VolatilityHeston with jumps Volatiltity
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74/85
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90.11
0.115
0.12
0.125
0.13
0.135
Delta
V o
l a t i l i t y
Volatilities on EUR/USD FX Options for maturity of 1 year
Market VolatilityHeston with jumps Volatiltity
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90.11
0.115
0.12
0.125
0.13
0.135
Delta
V o
l a t i l i t y
Volatilities on EUR/USD FX Options for maturity of 2 years
Market VolatilityHeston with jumps Volatiltity
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0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
0.13
0.14
0.15
0.16
0.17
0.18
Delta
V o
l a t i l i t y
Volatilities on EUR/JPY FX Options for maturity of 1 month
Market VolatilityHeston with jumps Volatiltity
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
0.13
0.14
0.15
0.16
0.17
0.18
Delta
V o
l a t i l i t y
Volatilities on EUR/JPY FX Options for maturity of 3 months
Market VolatilityHeston with jumps Volatiltity
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76/85
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
0.13
0.14
0.15
0.16
0.17
0.18
Delta
V o
l a t i l i t y
Volatilities on EUR/JPY FX Options for maturity of 6 months
Market VolatilityHeston with jumps Volatiltity
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
0.13
0.14
0.15
0.16
0.17
0.18
Delta
V o
l a t i l i t y
Volatilities on EUR/JPY FX Options for maturity of 2 years
Market VolatilityHeston with jumps Volatiltity
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