Bond plus option: Difference between revisions
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{{More citations needed|date=December 2022}} |
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In finance, a '''Bond+Option''' is a [[capital guarantee]] product that provides an investor with a fixed, predetermined '''participation''' to an [[option (finance)|option]]. Buying the [[zero-coupon bond]] ensures the guarantee of the capital, and the remaining proceeds are used to buy an option. |
In finance, a '''Bond+Option''' is a [[capital guarantee]] product that provides an investor with a fixed, predetermined '''participation''' to an [[option (finance)|option]]. Buying the [[zero-coupon bond]] ensures the guarantee of the capital, and the remaining proceeds are used to buy an option.<ref>{{Cite web |title=Zero-Coupon Bond: Definition, How It Works, and How To Calculate |url=https://www.investopedia.com/terms/z/zero-couponbond.asp |access-date=2017-03-07 |website=Investopedia |language=en}}</ref> |
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==Structure== |
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As an example, we can consider a bond+call on 5 years, with [[Nokia]] as an [[underlying]]. Say it is a USD [[currency]] option, and that 5 year rates are 4.7%. That gives you a [[zero-coupon bond]] price of <math>ZCB(USD,5y,4.7\%)=e^{-5*0.047}\approx0.7906</math>. |
As an example, we can consider a bond+call on 5 years, with [[Nokia]] as an [[underlying]]. Say it is a USD [[currency]] option, and that 5 year rates are 4.7%. That gives you a [[zero-coupon bond]] price of <math>ZCB(USD,5y,4.7\%)=e^{-5*0.047}\approx0.7906</math>. |
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Say we are counting in units of $100. We then have to buy $79.06 worth of |
Say we are counting in units of $100. We then have to buy $79.06 worth of bonds to guarantee the 100 to be repaid at maturity, and we have $20.94 to spend on an option. Now the option price is unlikely to be exactly equal to 20.94 in this case, and it really depends on the underlying. Say we are using the [[Black–Scholes]] price for the call, and that we strike the option [[at the money]], the [[Volatility (finance)|volatility]] is the defining part here. A call on an underlying with [[implied volatility]] of 25% will give you a [[Black–Scholes]] price of $15.7 while with a volatility of 45%, you'd have to pay $21.76.<ref>{{Cite web |title=Black-Scholes-Merton {{!}} Brilliant Math & Science Wiki |url=https://brilliant.org/wiki/black-scholes-merton/ |access-date=2017-03-07 |website=brilliant.org |language=en-us}}</ref> |
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Hence the '''participation''' would be the proportion you can get with the money you have. |
Hence the '''participation''' would be the proportion you can get with the money you have. |
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* In the 25% vol case you get a 133% participation |
* In the 25% vol case you get a 133% participation |
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* In the 45% vol case, 96%. |
* In the 45% vol case, 96%. |
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The alternative is to simply buy the bond, which would return $126.49. |
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==References== |
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{{Reflist}} |
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{{DEFAULTSORT:Bond Plus Option}} |
{{DEFAULTSORT:Bond Plus Option}} |
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[[Category:Bonds]] |
[[Category:Bonds (finance)]] |
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[[Category:Derivatives (finance)]] |
[[Category:Derivatives (finance)]] |
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[[sv:Deltagandegrad]] |
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[[tr:Katılım bankacılığı]] |
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Latest revision as of 03:13, 7 January 2023
 | This article needs additional citations for verification. (December 2022) |
In finance, a Bond+Option is a capital guarantee product that provides an investor with a fixed, predetermined participation to an option. Buying the zero-coupon bond ensures the guarantee of the capital, and the remaining proceeds are used to buy an option.[1]
Structure
[edit]As an example, we can consider a bond+call on 5 years, with Nokia as an underlying. Say it is a USD currency option, and that 5 year rates are 4.7%. That gives you a zero-coupon bond price of .
Say we are counting in units of $100. We then have to buy $79.06 worth of bonds to guarantee the 100 to be repaid at maturity, and we have $20.94 to spend on an option. Now the option price is unlikely to be exactly equal to 20.94 in this case, and it really depends on the underlying. Say we are using the Black–Scholes price for the call, and that we strike the option at the money, the volatility is the defining part here. A call on an underlying with implied volatility of 25% will give you a Black–Scholes price of $15.7 while with a volatility of 45%, you'd have to pay $21.76.[2]
Hence the participation would be the proportion you can get with the money you have.
- In the 25% vol case you get a 133% participation
- In the 45% vol case, 96%.
The alternative is to simply buy the bond, which would return $126.49.
References
[edit]- ^ "Zero-Coupon Bond: Definition, How It Works, and How To Calculate". Investopedia. Retrieved 2017-03-07.
- ^ "Black-Scholes-Merton | Brilliant Math & Science Wiki". brilliant.org. Retrieved 2017-03-07.