Pricing of Quanto Options

8/8/2019 Pricing of Quanto Options

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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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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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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


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



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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 2 years



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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



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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 year


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



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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


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



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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 6 months


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



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Pricing of Quanto Options

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