<Text-field style="Heading 1" layout="Heading 1"><Font italic="true">Economy A</Font></Text-field>

We first introduce the exchange rate process LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEjWFRGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjNRJ25vcm1hbEYn - as the rate that converts the B-economy payoffs into A-economy currency: Example: 1US$ = 110 JPY

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JlEjWDBGJy8lJ2l0YWxpY0dRJXRydWVGJy8lK2ZvcmVncm91bmRHUS1bMTUzLDUxLDEwMl1GJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjZRJ25vcm1hbEYn = current exchange rate; \316\264 is the drift of the process; \316\267 is the volatility of the process and \317\201 is the correlation of exchange rate process with the B-economy stock price.

QyQ+SSNYVEc2IiomSSNYMEdGJSIiIi1JJGV4cEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYjLCYqJiwmSSZkZWx0YUdGJUYoKiRJJGV0YUdGJSIiIyMhIiJGNUYoSSJ0R0YlRihGKCooRjRGKC1JJXNxcnRHRis2I0Y4RihJI1IzR0YlRihGKEYoRig=

KiZJI1gwRzYiIiIiLUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMsJiomLCZJJmRlbHRhR0YkRiUqJEkkZXRhR0YkIiIjIyEiIkYyRiVJInRHRiRGJUYlKihGMUYlRjUjRiVGMiwmKiZJJHJob0dGJEYlSSNfUkc2JUYpSS9SYW5kb21WYXJpYWJsZUdGJEk5X1Byb2JhYmlsaXR5RGlzdHJpYnV0aW9uR0YkRiVGJSomLCZGJUYlKiRGOkYyRjRGN0kkX1IwRzYlRilGPUk6X1Byb2JhYmlsaXR5RGlzdHJpYnV0aW9uMEdGJEYlRiVGJUYlRiU=

Our objective is to find a probability measure s.t. the B-economy asset process normalized by the A-economy market rate is martingale. For this, we first need to find the risk-neutral process for LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEjWFRGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjNRJ25vcm1hbEYn. We will find it by normalizing the B-economy money market fund by A-economy rate: This is 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

QyQ+SSVCWEJQRzYiLUklZXZhbEclKnByb3RlY3RlZEc2JC1JLkV4cGVjdGVkVmFsdWVHRiU2IyooJkkjQlRHRiU2I0kiQkdGJSIiIkkjWFRHRiVGMiZGLzYjSSJBR0YlISIiNyQvJkkjQjBHRiVGNUYyLyZGO0YwRjJGMg==

KiYtSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IywoKiYmSSJyR0YoNiNJIkJHRigiIiJJInRHRihGMEYwKiZGMUYwSSZkZWx0YUdGKEYwRjAqJiZGLTYjSSJBR0YoRjBGMUYwISIiRjBJI1gwR0YoRjA=

Under original measure P, this is not martingale, so using Girsanov we transform the Wiener process to a new measure LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkmbW92ZXJHRiQ2JS1JI21pR0YkNiVRIlBGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2JS1JI21vR0YkNi1RIl5GJy9GNlEnbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRkIvJSlzdHJldGNoeUdGQi8lKnN5bW1ldHJpY0dGQi8lKGxhcmdlb3BHRkIvJS5tb3ZhYmxlbGltaXRzR0ZCLyUnYWNjZW50R0ZCLyUnbHNwYWNlR1EsMC4xMTExMTExZW1GJy8lJ3JzcGFjZUdGUUYyRjUvJSdhY2NlbnRHRjRGPg== by imposing: LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkmbW92ZXJHRiQ2JS1GIzYlLUkjbWlHRiQ2JVEjUjNGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRidGNEY3LUYjNiUtSSNtb0dGJDYtUSomdW1pbnVzMDtGJy9GOFEnbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRkQvJSlzdHJldGNoeUdGRC8lKnN5bW1ldHJpY0dGRC8lKGxhcmdlb3BHRkQvJS5tb3ZhYmxlbGltaXRzR0ZELyUnYWNjZW50R0ZELyUnbHNwYWNlR1EsMC4yMjIyMjIyZW1GJy8lJ3JzcGFjZUdGU0Y0RjcvJSdhY2NlbnRHRjZGQA==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 where \316\261 satisfies : 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

Qyo+SSVzb2xuRzYiLUkmc29sdmVHRiU2JC8sKiZJInJHRiU2I0kiQkdGJSIiIiZGLDYjSSJBR0YlISIiSSZkZWx0YUdGJUYvKiZJJGV0YUdGJUYvSSZhbHBoYUdGJUYvRi8iIiFGN0YvPkklWFRQMUdGJSomSSNYMEdGJUYvLUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YlNiMsJiomLCZGNEYvKiRGNiIiIyNGM0ZHRi9JInRHRiVGL0YvKihGNkYvLUklc3FydEdGPzYjRklGLywmSSNSM0dGJUYvKiZGJEYvRktGL0YvRi9GL0YvRi8+SSdFVlhUUDFHRiUtSS5FeHBlY3RlZFZhbHVlR0YlNiNGOkYvLUklZXZhbEdGQDYkLUZUNiMqKCZJI0JUR0YlRi1GL0Y6Ri8mRmduRjFGMzckLyZJI0IwR0YlRjFGLy8mRlxvRi1GL0Yv

LCQqJiwoJkkickc2IjYjSSJCR0YnIiIiJkYmNiNJIkFHRichIiJJJmRlbHRhR0YnRipGKkkkZXRhR0YnRi5GLg==

KiZJI1gwRzYiIiIiLUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMsJiomLCZJJmRlbHRhR0YkRiUqJEkkZXRhR0YkIiIjIyEiIkYyRiVJInRHRiRGJUYlKihGMUYlRjUjRiVGMiwoKiZJJHJob0dGJEYlSSNfUkc2JUYpSS9SYW5kb21WYXJpYWJsZUdGJEk5X1Byb2JhYmlsaXR5RGlzdHJpYnV0aW9uR0YkRiVGJSomLCZGJUYlKiRGOkYyRjRGN0kkX1IwRzYlRilGPUk6X1Byb2JhYmlsaXR5RGlzdHJpYnV0aW9uMEdGJEYlRiUqKCwoJkkickdGJDYjSSJCR0YkRiUmRkg2I0kiQUdGJEY0Ri9GJUYlRjFGNEY1RjdGNEYlRiVGJQ==

KiYtSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IywmKiYmSSJyR0YoNiNJIkJHRigiIiJJInRHRihGMCEiIiomJkYtNiNJIkFHRihGMEYxRjBGMEYwSSNYMEdGKEYw

SSNYMEc2Ig==

The results above show that under the new probability measure LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkmbW92ZXJHRiQ2JS1JI21pR0YkNiVRIlBGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2JS1JI21vR0YkNi1RIl5GJy9GNlEnbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRkIvJSlzdHJldGNoeUdGQi8lKnN5bW1ldHJpY0dGQi8lKGxhcmdlb3BHRkIvJS5tb3ZhYmxlbGltaXRzR0ZCLyUnYWNjZW50R0ZCLyUnbHNwYWNlR1EsMC4xMTExMTExZW1GJy8lJ3JzcGFjZUdGUUYyRjUvJSdhY2NlbnRHRjRGPg== is exchange rate process has the risk-neutral drift of 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, and when normalized by the two money-market funds, the process is martingale.

One issue we need to resolve is the drift for the exchange rates process. Using interest rate parity and the example above, we can establish:

QyY+SSh4dGRyaWZ0RzYiKiYtSSlzaW1wbGlmeUc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYkLUkjbG5HRiU2IyomLUkuRXhwZWN0ZWRWYWx1ZUdGJTYjSSVYVFAxR0YlIiIiSSNYMEdGJSEiIkkpc3ltYm9saWNHRiVGNUkidEdGJUY3RjU+SSVYVFAyR0YlLUklc3Vic0dGKjYkL0kmZGVsdGFHRiVGJEkjWFRHRiVGNQ==

LCYmSSJyRzYiNiNJIkJHRiUhIiImRiQ2I0kiQUdGJSIiIg==

KiZJI1gwRzYiIiIiLUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMsJiomLCgmSSJyR0YkNiNJIkJHRiQhIiImRjA2I0kiQUdGJEYlKiRJJGV0YUdGJCIiIyNGM0Y5RiVJInRHRiRGJUYlKihGOEYlRjsjRiVGOSwmKiZJJHJob0dGJEYlSSNfUkc2JUYpSS9SYW5kb21WYXJpYWJsZUdGJEk5X1Byb2JhYmlsaXR5RGlzdHJpYnV0aW9uR0YkRiVGJSomLCZGJUYlKiRGQEY5RjNGPUkkX1IwRzYlRilGQ0k6X1Byb2JhYmlsaXR5RGlzdHJpYnV0aW9uMEdGJEYlRiVGJUYlRiU=

How about the Q-measure for the exchange rate process? We know that under Q, the process must be driftless, so we may state:

Qyw+SShzdGRyaWZ0RzYiLUkmc29sdmVHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiU2JC8sJkkoeHRkcmlmdEdGJSIiIiomSSRldGFHRiVGL0kjbnVHRiVGL0YvIiIhRjJGLz5JJVhUUDNHRiUtSSVzdWJzR0YpNiQ8JC9JI1IzR0YlLCZGO0YvKiZGJEYvLUklc3FydEdGKDYjSSJ0R0YlRi9GLy9JJmRlbHRhR0YlRi5JI1hUR0YlRi8tSS5FeHBlY3RlZFZhbHVlR0YlNiNGNUYvPkkkWFRRR0YlLUY3NiQ8JC8mSSJyR0YlNiNJIkFHRiVGMy8mRk82I0kiQkdGJUYzSSVYVFAyR0YlRi8tRkY2I0ZJRi8=

LCQqJiwmJkkickc2IjYjSSJCR0YnISIiJkYmNiNJIkFHRiciIiJGLkkkZXRhR0YnRipGKg==

KiZJI1gwRzYiIiIiLUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMsJiomLCgmSSJyR0YkNiNJIkJHRiQhIiImRjA2I0kiQUdGJEYlKiRJJGV0YUdGJCIiIyNGM0Y5RiVJInRHRiRGJUYlKihGOEYlRjsjRiVGOSwoKiZJJHJob0dGJEYlSSNfUkc2JUYpSS9SYW5kb21WYXJpYWJsZUdGJEk5X1Byb2JhYmlsaXR5RGlzdHJpYnV0aW9uR0YkRiVGJSomLCZGJUYlKiRGQEY5RjNGPUkkX1IwRzYlRilGQ0k6X1Byb2JhYmlsaXR5RGlzdHJpYnV0aW9uMEdGJEYlRiUqKCwmRi9GM0Y0RiVGJUY4RjNGO0Y9RjNGJUYlRiU=

SSNYMEc2Ig==

KiZJI1gwRzYiIiIiLUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMsJiomSSJ0R0YkRiVJJGV0YUdGJCIiIyMhIiJGMCooRi9GJUYuI0YlRjAsJiomSSRyaG9HRiRGJUkjX1JHNiVGKUkvUmFuZG9tVmFyaWFibGVHRiRJOV9Qcm9iYWJpbGl0eURpc3RyaWJ1dGlvbkdGJEYlRiUqJiwmRiVGJSokRjdGMEYyRjRJJF9SMEc2JUYpRjpJOl9Qcm9iYWJpbGl0eURpc3RyaWJ1dGlvbjBHRiRGJUYlRiVGJUYl

SSNYMEc2Ig==

We can now define a B-economy stock price process in A-economy currency Example: US stock price process expressed in JPY

What is the process for such "hybrid" instrument? Since change of measure affects the drift but keeps volatility intact, we may write this process in the differential form as: 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 where LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnJiM5NDY7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Yy is the drift we need to find

QyQ+SSVTVDJCRzYiKiZJI1MwR0YlIiIiLUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YlNiMsJiomLCZJJ2xhbWJkYUdGJUYoKiRJJnNpZ21hR0YlIiIjIyEiIkY1RihJInRHRiVGKEYoKihGNEYoLUklc3FydEdGKzYjRjhGKEkjUjFHRiVGKEYoRihGKA==

KiZJI1MwRzYiIiIiLUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMsJiomLCZJJ2xhbWJkYUdGJEYlKiRJJnNpZ21hR0YkIiIjIyEiIkYyRiVJInRHRiRGJUYlKihGMUYlRjUjRiVGMkkjX1JHNiVGKUkvUmFuZG9tVmFyaWFibGVHRiRJOV9Qcm9iYWJpbGl0eURpc3RyaWJ1dGlvbkdGJEYlRiVGJQ==

QyQ+SSVTWEJQRzYiLUklZXZhbEclKnByb3RlY3RlZEc2JComLUkuRXhwZWN0ZWRWYWx1ZUdGJTYjKihJJVNUMkJHRiUiIiJJJFhUUUdGJUYwJkkjQlRHRiU2I0kiQkdGJSEiIkYwSSNYMEdGJUY2NyQvJkkjQjBHRiU2I0kiQUdGJUYwLyZGO0Y0RjBGMA==

KiYtSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IywoKiZJInRHRigiIiJJJ2xhbWJkYUdGKEYtRi0qJiZJInJHRig2I0kiQkdGKEYtRixGLSEiIioqSSZzaWdtYUdGKEYtRixGLUkkZXRhR0YoRi1JJHJob0dGKEYtRi1GLUkjUzBHRihGLQ==

QyY+SShzeGRyaWZ0RzYiKiYtSSlzaW1wbGlmeUc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYkLUkjbG5HRik2IyomSSVTWEJQR0YlIiIiSSNTMEdGJSEiIkkpc3ltYm9saWNHRiVGMkkidEdGJUY0RjI+SSdsYW1iZGFHRiUtSSZzb2x2ZUdGKTYkL0YkIiIhRjhGMg==

LChJJ2xhbWJkYUc2IiIiIiZJInJHRiQ2I0kiQkdGJCEiIiooSSZzaWdtYUdGJEYlSSRldGFHRiRGJUkkcmhvR0YkRiVGJQ==

LCYmSSJyRzYiNiNJIkJHRiUiIiIqKEkmc2lnbWFHRiVGKEkkZXRhR0YlRihJJHJob0dGJUYoISIi

This is the desired result - the Quanto-adjusted forward rate of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEjU1RGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjNRJ25vcm1hbEYn. It shows that under Q measure and Quanto transformation all we need is the adjust the B-economy stock price drift by \316\273 factor. Then under Q, 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is:

QyY+SSVFUVNURzYiLUkuRXhwZWN0ZWRWYWx1ZUdGJTYjSSVTVDJCR0YlIiIiPkklU1RRQkdGJS1JJXN1YnNHJSpwcm90ZWN0ZWRHNiQvSSNSMUdGJUkieUdGJUYpRio=

KiYtSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IywmKiYmSSJyR0YoNiNJIkJHRigiIiJJInRHRihGMEYwKipJJnNpZ21hR0YoRjBGMUYwSSRldGFHRihGMEkkcmhvR0YoRjAhIiJGMEkjUzBHRihGMA==

KiZJI1MwRzYiIiIiLUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMsJiomLCgmSSJyR0YkNiNJIkJHRiRGJSooSSZzaWdtYUdGJEYlSSRldGFHRiRGJUkkcmhvR0YkRiUhIiIqJEY0IiIjI0Y3RjlGJUkidEdGJEYlRiUqKEY0RiVGOyNGJUY5SSJ5R0YkRiVGJUYl

Once we have established the Quanto stock price process, we can now value a Quanto Option:

Quanto Call on B-economy stock price expressed in A-economy currency: This is LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEjWDBGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYtUScmc2RvdDtGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGTEY5 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

Quanto call payoff reduces to 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 One may notice that the exchange rate is now deterministic and enters the formula as parameter rather than variable. Quanto options exist in many variations - the most common is the setting of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEjWDBGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYtUSJ+RicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y9LyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRkwtRjY2LVEiPUYnRjlGO0Y+RkBGQkZERkZGSC9GS1EsMC4yNzc3Nzc4ZW1GJy9GTkZTLUkjbW5HRiQ2JFEiMUYnRjlGOQ== which implies that the option pays exactly the same amount as in the B-economy, however expressed in A-economy currency. However, we can use any other translation factor - eg. spot exchange rate - to express the option payoff in the foreign currency.

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

LCQqKCwqKiYmSSJyRzYiNiNJIkJHRigiIiJJInRHRihGKyEiIyoqSSZzaWdtYUdGKEYrRixGK0kkZXRhR0YoRitJJHJob0dGKEYrIiIjKiZGLEYrRi9GMkYrLUkjbG5HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRig2IyomSSJLR0YoRitJI1MwR0YoISIiRjJGK0YvRj1GLCNGPUYyI0YrRjI=

LCQqKi1JJGV4cEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjLCQqJiZJInJHRik2I0kiQUdGKSIiIkkidEdGKUYxISIiRjFJI1gwR0YpRjEsKiooSSNTMEdGKUYxLUYlNiMqJiZGLjYjSSJCR0YpRjFGMkYxRjEtSSRlcmZHRiY2IywkKioiIiMjRjFGQywqLUkjbG5HRiY2IyomSSJLR0YpRjFGN0YzRkNGOiEiIyoqSSZzaWdtYUdGKUYxRjJGMUkkZXRhR0YpRjFJJHJob0dGKUYxRkMqJkYyRjFGTUZDRjNGMUZNRjNGMiNGM0ZDI0YxIiIlRjFGMyooRkpGMS1GPzYjLCQqKiwqRjpGS0ZMRkNGUEYxRkZGQ0YxRk1GM0YyRlFGQ0ZERlJGMS1GJTYjRkxGMUYxKiZGN0YxRjhGMUYxKiZGSkYxRlpGMUYzRjEtRiU2IywkRkxGM0YxRkQ=

LCQqKi1JJGV4cEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjLCQqJiZJInJHRik2I0kiQUdGKSIiIkkidEdGKUYxISIiRjFJI1gwR0YpRjEsKiomSSJLR0YpRjEtRiU2IyoqSSZzaWdtYUdGKUYxRjJGMUkkZXRhR0YpRjFJJHJob0dGKUYxRjFGMSomSSNTMEdGKUYxLUYlNiMqJiZGLjYjSSJCR0YpRjFGMkYxRjFGMyooRjdGMS1JJGVyZkdGJjYjLCQqKiwqRkIhIiNGOiIiIyomRjJGMUY7Rk5GMS1JI2xuR0YmNiMqJkY3RjFGP0YzRk5GMUY7RjNGMiNGM0ZORk4jRjFGTiNGMSIiJUYxRjhGMUYxKihGP0YxRkBGMS1GSDYjLCQqKkZORlUsKkZQRk5GQkZNRjpGTkZPRjNGMUY7RjNGMkZURlZGMUYzRjEtRiU2IywkRjpGM0YxRlU=

QyY+JkkrTnVtUmVzQ2FsbEc2IjYjSSRKUFlHRiYtSSZldmFsZkclKnByb3RlY3RlZEc2Iy1JJWV2YWxHRis2JEkmUUNhbGxHRiY3Ky9JI1MwR0YmIiM1L0kiS0dGJkY0L0kidEdGJiIiIi9JJnNpZ21hR0YmJCIjRCEiIy9JJGV0YUdGJiQiIzdGPi9JJHJob0dGJiQiIichIiIvJkkickdGJjYjSSJCR0YmJCIiJEY+LyZGSjYjSSJBR0YmJEY5Rj4vSSNYMEdGJiIkNSJGOT4mSSpOdW1SZXNQdXRHRiZGJy1GKjYjLUYuNiRJJVFQdXRHRiZGMUY5

JCIrUCF5bzoiISIo

JCIrKj0vYS0iISIo

JSFH

This is the premium of Quanto Call / Put in Japanese Yen on US Stock with current price of $10 and identical strike. The example assumes that the exchange rate is $1 = 110 JPY

QyQtSSdwbG90M2RHNiI2Jy1JJWV2YWxHJSpwcm90ZWN0ZWRHNiRJJlFDYWxsR0YlNykvSSNTMEdGJSIjNS9JIktHRiVGLy9JInRHRiUiIiIvSSZzaWdtYUdGJSQiI0QhIiMvJkkickdGJTYjSSJCR0YlJCIiJEY5LyZGPDYjSSJBR0YlJCIjOiEiJC9JI1gwR0YlIiQ1Ii9JJGV0YUdGJTskIiIjRjkkRk8hIiIvSSRyaG9HRiU7JCEiJ0ZRJCIiJ0ZRL0klYXhlc0dGJVEnZnJhbWVkRiUvSSZ0aXRsZUdGJTckUVZRdWFudG9+Q2FsbH4tfmNvcnJlbGF0aW9ufmFuZH5GWH52b2xhdGlsaXR5fmltcHBhY3R+fkYlL0klZm9udEdGJTclSSZUSU1FU0dGJUklQk9MREdGJSIjN0Y0

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-%&TITLEG6$QVQuanto~Call~-~correlation~and~FX~volatility~imppact~~6"-I%FONTG6"6%I&TIMESG6"I%BOLDG6""#7-%,ORIENTATIONG6$$"#I!""$"$S'!""

We can extend the concept of Quanto Option into a different type of option where we make the exchange rate stochastic. These options are usually known as Compo Options.

The Compo Call payoff is: 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 where LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiS0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUYvNiVRIkFGJ0YyRjVGMkY1LyUvc3Vic2NyaXB0c2hpZnRHUSIwRicvRjZRJ25vcm1hbEYn is the strike price in the A-economy currency

We need to determine the joint process for B-economy stock price and the exchange rate:

We will find the first two moments of the joint distribution:

Qyo+SSRTVFFHNiItSSVzdWJzRyUqcHJvdGVjdGVkRzYkL0kjbXVHRiUiIiFJI1NUR0YlIiIiPkkmSlRlcm1HRiUtSSlzaW1wbGlmeUc2JEYoSShfc3lzbGliR0YlNiQtSSNsbkdGMzYjKipGJEYuSSNTMEdGJSEiIkkkWFRRR0YlRi5JI1gwR0YlRjtJKXN5bWJvbGljR0YlRjs+SSdTWE1lYW5HRiUtSS5FeHBlY3RlZFZhbHVlR0YlNiNGMEYuPkkmU1hWYXJHRiUtRjI2IyomLUkpVmFyaWFuY2VHRiVGQ0YuSSJ0R0YlRjtGLg==

KiZJI1MwRzYiIiIiLUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMsJiomSSJ0R0YkRiVJJnNpZ21hR0YkIiIjIyEiIkYwKihGL0YlRi4jRiVGMEkjX1JHNiVGKUkvUmFuZG9tVmFyaWFibGVHRiRJOV9Qcm9iYWJpbGl0eURpc3RyaWJ1dGlvbkdGJEYlRiVGJQ==

LCYqJkkidEc2IiIiIkkmc2lnbWFHRiUiIiMjISIiRigqJkYkRiZJJGV0YUdGJUYoRik=

LCgqJEkmc2lnbWFHNiIiIiMiIiIqKEYkRidJJGV0YUdGJUYnSSRyaG9HRiVGJ0YmKiRGKUYmRic=

This shows that the joint distribution of 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

QyQ+SSRTVEpHNiIqKEkjUzBHRiUiIiJJI1gwR0YlRigtSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiU2IywmSSdTWE1lYW5HRiVGKCooLUklc3FydEdGLDYjSSZTWFZhckdGJUYoLUY0NiNJInRHRiVGKEkieUdGJUYoRihGKEYo

KihJI1MwRzYiIiIiSSNYMEdGJEYlLUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMsKComSSJ0R0YkRiVJJnNpZ21hR0YkIiIjIyEiIkYxKiZGL0YlSSRldGFHRiRGMUYyKigsKCokRjBGMUYlKihGMEYlRjVGJUkkcmhvR0YkRiVGMSokRjVGMUYlI0YlRjFGL0Y8SSJ5R0YkRiVGJUYl

QyQ+SSdjcnZhbDJHNiItSSZzb2x2ZUc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYkL0kkU1RKR0YlSSJLR0YlSSJ5R0YlIiIi

LCQqKCwoKiZJInRHNiIiIiJJJnNpZ21hR0YnIiIjRigqJkYmRihJJGV0YUdGJ0YqRigtSSNsbkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJzYjKihJIktHRidGKEkjUzBHRichIiJJI1gwR0YnRjZGKkYoLCgqJEYpRipGKCooRilGKEYsRihJJHJob0dGJ0YoRioqJEYsRipGKCNGNkYqRiZGPSNGKEYq

QyY+JkkmUUNhbGxHNiI2IyIiIy1JKWFzc3VtaW5nR0koX3N5c2xpYkdGJjYkNyMqJi1JJGV4cEc2JCUqcHJvdGVjdGVkR0YrNiMsJComJkkickdGJjYjSSJBR0YmIiIiSSJ0R0YmRjohIiJGOi1JJGludEdGMTYkKigsJkkkU1RKR0YmRjpJIktHRiZGPEY6LUYwNiMsJCokSSJ5R0YmRigjRjxGKEY6LUklc3FydEdGMTYjLCRJI1BpR0YyRihGPC9GSDtJJ2NydmFsMkdGJkkpaW5maW5pdHlHRjJGOjcmLUkiPkdGMjYkRjsiIiEtRlU2JEkmc2lnbWFHRiZGVy1GVTYkSSRldGFHRiZGVy1GVTYkRjZGV0Y6PiZJJVFQdXRHRiZGJy1GKjYkNyMqJkYvRjotRj42JCooLCZGQ0Y6RkJGPEY6RkRGOkZKRjwvRkg7LCRGUkY8RlFGOkZTRjo=

KiYtSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IywkKiYmSSJyR0YoNiNJIkFHRigiIiJJInRHRihGMCEiIkYwLCoqKkkjUzBHRihGMEkjWDBHRihGMC1GJDYjKipJJnNpZ21hR0YoRjBGMUYwSSRldGFHRihGMEkkcmhvR0YoRjBGMC1JJGVyZkdGJTYjLCQqKiIiIyNGMEZCLCpGOSEiJSomRjFGMEY6RkJGMiomRjFGMEY7RkJGMi1JI2xuR0YlNiMqKEkiS0dGKEYwRjVGMkY2RjJGQkYwLCgqJEY6RkJGMCooRjpGMEY7RjBGPEYwRkIqJEY7RkJGMCNGMkZCRjFGUSNGMCIiJUYwRlEqJkZMRjAtRj42IywkKiosKEZGRjBGR0YwRkhGQkYwRk1GUUYxRlFGQkZDRlJGMEZDKihGNUYwRjZGMEY3RjBGQ0ZMRlFGMA==

KiYtSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IywkKiYmSSJyR0YoNiNJIkFHRigiIiJJInRHRihGMCEiIkYwLCpJIktHRigjRjAiIiMqKEkjUzBHRihGMEkjWDBHRihGMC1GJDYjKipJJnNpZ21hR0YoRjBGMUYwSSRldGFHRihGMEkkcmhvR0YoRjBGMCNGMkY2KiZGNEYwLUkkZXJmR0YlNiMsJCoqLCgqJkYxRjBGPUY2RjAqJkYxRjBGPkY2RjAtSSNsbkdGJTYjKihGNEYwRjhGMkY5RjJGNkYwLCgqJEY9RjZGMCooRj1GMEY+RjBGP0YwRjYqJEY+RjZGMEZARjFGQEY2RjUjRjAiIiVGMEY1KipGOEYwRjlGMEY6RjAtRkM2IywkKipGNkY1LCpGPCEiJUZIRjJGSUYyRkpGNkYwRk5GQEYxRkBGUkYwRkBGMA==

These are the values of Compo's Call and Put. Having obtained the closed-from solution, we can determine the option's sensitivity w.r.t correlation:

QyY+SSVEUmhvRzYiLUklZGlmZkclKnByb3RlY3RlZEc2JCZJJlFDYWxsR0YlNiMiIiNJJHJob0dGJSIiIi1JJXBsb3RHRiU2JS1JJWV2YWxHRig2JEYkNyovSSNTMEdGJSIjNS9JIktHRiUiJSs2L0kidEdGJUYvL0kmc2lnbWFHRiUkIiNEISIjL0kkZXRhR0YlJCIjPUZDLyZJInJHRiU2I0kiQkdGJSQiIiRGQy8mRko2I0kiQUdGJSQiIzohIiQvSSNYMEdGJSIkNSIvRi47JCEiKSEiIiQiIilGZ24vSSZ0aXRsZUdGJTckUUdDb21wb35DYWxsfi1+Y29ycmVsYXRpb25+c2Vuc2l0aXZpdHl+fkYlL0klZm9udEdGJTclSSZUSU1FU0dGJUklQk9MREdGJSIjN0Yv

KiYtSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IywkKiYmSSJyR0YoNiNJIkFHRigiIiJJInRHRihGMCEiIkYwLCoqMEkjUzBHRihGMEkjWDBHRihGMEkmc2lnbWFHRihGMEYxRjBJJGV0YUdGKEYwLUYkNiMqKkY3RjBGMUYwRjhGMEkkcmhvR0YoRjBGMC1JJGVyZkdGJTYjLCQqKiIiIyNGMEZCLCpGOyEiJSomRjFGMEY3RkJGMiomRjFGMEY4RkJGMi1JI2xuR0YlNiMqKEkiS0dGKEYwRjVGMkY2RjJGQkYwLCgqJEY3RkJGMCooRjdGMEY4RjBGPEYwRkIqJEY4RkJGMCNGMkZCRjFGUSNGMCIiJUYwRlEqLkY1RjBGNkYwRjlGMEkjUGlHRiZGUS1GJDYjLCQqKEZERkJGTUYyRjFGMiNGMiIiKUYwLCYqLEZCRkNGN0YwRjFGQ0Y4RjBGTUZRRjIqLkZCRkNGREYwRk0jISIkRkJGMUZRRjdGMEY4RjAjRjJGU0YwRjIqNEZMRjBGVUZRLUYkNiMsJCooLChGRkYwRkdGMEZIRkJGQkZNRjJGMUYyRlpGMEZhb0YwRk1GaW5GMUZRRkJGQ0Y3RjBGOEYwRltvKi5GNUYwRjZGMEY3RjBGMUYwRjhGMEY5RjBGQ0Yw

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

As the graph shows, the correlation is significant valuation factor: negative correlation between the stock price and the exchange rate will increase the option premium, while positive correlation will push it lower. This is intuitive - positive correlation increases the volatility of joint distribution which leads to higher option premium.

QyY+JkkrTnVtUmVzQ2FsbEc2IjYjSSRKUFlHRiYtSSZldmFsZkclKnByb3RlY3RlZEc2Iy1JJWV2YWxHRis2JCZJJlFDYWxsR0YmNiMiIiM3Ky9JI1MwR0YmIiM1L0kiS0dGJiIlKzYvSSJ0R0YmIiIiL0kmc2lnbWFHRiYkIiNEISIjL0kkZXRhR0YmJCIjN0ZCL0kkcmhvR0YmJCIiJyEiIi8mSSJyR0YmNiNJIkJHRiYkIiIkRkIvJkZONiNJIkFHRiYkRj1GQi9JI1gwR0YmIiQ1IkY9PiZJKk51bVJlc1B1dEdGJkYnLUYqNiMtRi42JCZJJVFQdXRHRiZGMkY0Rj0=

JCIrTiIpPW46ISIo

JCIrbExRcDghIig=