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Newton Raphson Starting Values

Yields

When calculating the yield of a bond, the Newton-Raphson iteration procedure uses the following seed value:

Equation Template

cpn = the periodic coupon payment.
CP = the clean price of the bond.
TTF = the time (in periods) to the next coupon payment.
n = the number of full coupon periods until the redemption date.

 

 

Implied Spot and Forward Prices

When calculating implied spot or forward prices, the Newton-Raphson iteration procedure uses the strike rate as the initial estimate of the spot/forward price.

 

 

Implied Strike Prices

When calculating implied strike prices, the Newton-Raphson iteration procedure uses the spot rate as the initial estimate of the strike price.

 

 

Implied Volatility

When calculating implied volatilities, the Newton-Raphson iteration procedure uses the Manaster and Koehler (1982) seed value as the initial estimate of the volatility. This is shown below:

Equation Template

S = spot/forward price of the underlying asset.
X = exercise price (strike).
r = risk-free interest rate, expressed with continuous compounding.
T = time to maturity measured in years (actual/365 basis).

 

 

Barone-Adesi Whaley Function

When calculating the critical spot prices the Newton-Raphson iteration procedure uses the Barone-Adesi Whaley seed value. This is shown below:

Equation Template

 

where Equation Template is the critical price when time to expiration is infinite:

Equation Template

b = cost of carry for the underlying asset, expressed with continuous compounding

See oBAW( ) Function

 

 

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