Converting from zero coupon rates and Derivative instrument: Difference between pages

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The zero coupon rate is also known as the [[zero coupon yield]], spot rate, or spot yield.
A derivative instrument or contract is one whose value and other characteristics are derived from those of another asset or instrument (sometimes known as the Underlying Asset).


Derivative instruments are widely used by non-financial corporates for hedging purposes.


'''Conversion'''


If we know the zero coupon rates (yield curve) for a given risk class and set of maturities, we can calculate both the [[forward yield]]s and the [[par yield]]s for the same maturities and risk class.
<span style="color:#4B0082">'''Example'''</span>


A share option is a type of derivative contract, allowing the holder to buy shares at a certain predetermined strike price.


The conversion process and calculation stems from the '[[no-arbitrage]]' relationship between the related yield curves.  
The value of the share option derives from the current price of the related underlying share relative to the option strike price.


This means - for example - that the total cumulative cash flows from a two-year investment must be identical, whether the investment is built:
* '[[Outright]]' from a two-year zero coupon investment
* Or as a [[synthetic]] deposit built using a forward contract, reinvesting intermediate principal and interest proceeds at a pre-agreed rate
* Or using a par investment, reinvesting intermediate interest to generate a total terminal cash flow
<span style="color:#4B0082">'''Example 1: Converting two-period zero coupon yields to forward yields'''</span>
Periodic zero coupon yields ('''z''') are:
z<sub>0-1</sub> = 0.02 per period (2%)
z<sub>0-2</sub> = 0.029951 per period (2.9951%)
The cash returned at Time 2 periods in the future, from investing £1m at Time 0 in a zero coupon instrument at a rate of 2.9951% per period, is:
£1m x 1.029951<sup>2</sup>
= £'''1.0608m'''
Under no-arbitrage pricing conditions, the identical terminal cash flow of £1.0608m results from investing in an outright zero coupon investment of one periods maturity, together with a forward contract for the second period - for reinvestment at the forward market yield of '''f<sub>1-2</sub>''' per period, as follows:
£1m x (1 + z<sub>0-1</sub>) x (1 + f<sub>1-2</sub>) = £'''1.0608m'''
Using this information, we can now calculate the forward yield for 1-2 periods' maturity.
1.02 x (1 + f<sub>1-2</sub>) = 1.0608
1 + f<sub>1-2</sub> = 1.0608 / 1.02
f<sub>1-2</sub> = (1.0608 / 1.02) - 1
= 1.04 - 1
= '''0.04''' per period (= 4%)
This is the market forward rate which we would enjoy if we were to pre-agree today, to make a one-period deposit, committing ourselves to put our money into the deposit one period in the future.
The no-arbitrage relationship says that making such a synthetic deposit should produce the identical terminal cash flow of £1.0608m. Let's see if that's borne out by our calculations.
Investing the same £1m in this synthetic two-periods maturity zero coupon instrument would return:
After one period: £1m x 1.02 = £1.02m
Reinvested for the second period at the pre-agreed rate of 0.04 per period for one more period:
= £1.02m x 1.04
= £'''1.0608m'''


== See also ==
* [[CertFMM]]
* [[Commodity risk]]
* [[CP]]
* [[Embedded derivative]]
* [[ETD]]
* [[FC]]
* [[Fixing instrument]]
* [[Hedge fund]]
* [[Hedging]]
* [[IR]]
* [[Maturity]]
* [[Notional principal]]
* [[Option]]
* [[Outright]]
* [[Strike price]]
* [[Tracker fund]]
* [[Transfer]]
* [[Underlying]]
* [[Underlying asset]]
* [[Underlying price]]
* [[XVA]]


''This is the same result as enjoyed from the outright zero coupon investment, as expected.


===Other links===
*[http://www.treasurers.org/node/8599  Masterclass: Derivatives, The Treasurer, December 2012]


*[http://www.treasurers.org/node/7849 Use and Misuse of Derivatives, Will Spinney, ACT 2012]


== See also ==
[[Category:Risk_frameworks]]
* [[Zero coupon yield]]
* [[Bootstrap]]
* [[Forward yield]]
* [[Par yield]]
* [[Coupon]]
* [[Spot rate]]
* [[Yield curve]]
* [[Zero]]
* [[Zero coupon bond]]
* [[Flat yield curve]]
* [[Rising yield curve]]
* [[Falling yield curve]]
* [[Positive yield curve]]
* [[Negative yield curve]]

Revision as of 12:01, 18 July 2016

A derivative instrument or contract is one whose value and other characteristics are derived from those of another asset or instrument (sometimes known as the Underlying Asset).

Derivative instruments are widely used by non-financial corporates for hedging purposes.


Example

A share option is a type of derivative contract, allowing the holder to buy shares at a certain predetermined strike price.

The value of the share option derives from the current price of the related underlying share relative to the option strike price.


See also


Other links

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