### Newton Raphson Starting Values

 Yields When calculating the yield of a bond, the Newton-Raphson iteration procedure uses the following seed value: 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: 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: where is the critical price when time to expiration is infinite: b = cost of carry for the underlying asset, expressed with continuous compounding Copyright 2013 Hedgebook Ltd.