Valuation model

What is the significance of this Here we take it as given that because price processes can be described as equivalent martingale measures (which we do not go into here) they enable the practitioner to construct a risk-free hedge of a market instmment. By enabling a no-arbitrage portfolio to be described, a mathematical model can be set up and solved, including risk-free valuation models. 

A key element of the description of a stochastic process is a specification of the level of informatimi oti the behaviour of prices that is available to an observer at each point in time. As with the martingale property, a calculation of the expected future values of a price process requires information on current prices. Generally, fmancial valuation models require data on both the current and the historical security prices, but investors are only able to deal on the basis of current known information and do not have access to future information. In a stochastic model, this concept is captured via the process known as filtration. 

All valuation models must capture a process describing the dynamics of the asset price. This was discussed at the start of the chapter and is a central tenet of derivative valuation models. Under the Black-Scholes model for example, the price dynamics of a risk-bearing asset St under the risk-neutral probability function Q are given by... 

In the following chapter, we tie in the work on dynamics of asset prices to option valuation models. 

Duffie, D., Kan, R., 1996. A yield-factor model of interest rates. Math. Financ. 6 (4), 379-406. Fitton, P., McNatt, J., 1997. The four faces of an interest rate model. In Fabozzi, F. (Ed.), Advances in Fixed Income Valuation Modelling and Risk Management. FJF Associates, New Hope, PA. 

The theory of options was developed in the assumption of market equilibrium. The first option pricing model was proposed by Black and Scholes (1973) and then by Merton (1973), in which they did not consider dividend payments. Authors as Schwartz (1975) include dividend payments into valuation model and also consider the possibility of exercising the option before the maturity... 

Convertible instruments are usually issued with attached call or put options. Such features can be implemented into the valuation model. If a soft call feature has been implemented, it enables the issuer to force the conversion when the share price overcomes a percentage or trigger level above the conversion price. However, this option cannot be called in the first years hard call . Differently, after the protection period, the issuer can exercise the option. This second time is referred to soft call . Using the same example shown in Section 9.3.1, we assume that the bond may be redeemed in whole but not in part at their principal amount plus accrued interest on the last 2 years, in which the maturity date is at 20 February 2019. On and after this call date , if the share price exceeds 130% of the conversion price the issuer can force the conversion. Figure 9.23 shows the stock price tree in which at years 4 and 5 the stock price is above the threshold. 

The option-adjusted spread (OAS) is the most important measure of risk for bonds with embedded options. It is the average spread required over the yield curve in order to take into account the embedded option element. This is, therefore, the difference between the yield of a bond with embedded option and a government benchmark bond. The spread incorporates the future views of interest rates and it can be determined with an iterative procedure in which the market price obtained by the pricing model is equal to expected cash flow payments (coupons and principal). Also a Monte Carlo simulation may be implemented in order to generate an interest rate path. Note that the option-adjusted spread is influenced by the parameters implemented into the valuation model as the yield curve, but above all by the volatility level assumed. This is referred to volatility dependent. The higher the volatility, the lower the option-adjusted spread for a callable bond and the higher for a putable bond. 

Despite its widespread use, the OAS has a number of limitations. Specifically, the OAS is model-dependent. Changing the assumptions of the valuation model may produce substantial differences in the computed OAS. 

There is another potential problem with using small rate shocks for complicated securities. The prices that are inserted into the duration formula as given by equation (4.1) are derived from a valuation model. The duration measure depends crucially on a valuation model. If the... 

There are valuation models that can be used to value bonds with embedded options. These models take into account how changes in yield will affect the expected cash flows. Thus, when V and V+ are the values produced from these valuation models, the resulting duration takes into account both the discounting at different interest rates and how the expected cash flows may change. When duration is calculated in this manner, it is referred to as effective duration or option-adjusted duration or OAS duration. Below we explain how effective duration is calculated based on the lattice model and the Monte Carlo model. 

Some market idiosyncrasies such as settlement conventions are an important part of a valuation model but irrelevant to a risk model. 

Interest Rate, Term Structure, and Valuation Modeling edited by Frank J. Fabozzi Investment Performance Measurement by Bruce J. Feibel The Handbook of Equity Style Management eAxteA by T. Daniel Coggin and Frank J. Fabozzi... 

The price of an option is composed of intrinsic value and time value. An option s intrinsic value is clear. Valuation models, therefore, essentially price time value. 

Effective duration is essentially approximate duration where P and P are obtained using a valuation model—such as a static cash flow model, a binomial model, or a simulation model—that incorporates the eflFect of a change in interest rates on the expected cash flows. The values of P and T, depend on the assumed prepayment rate. Generally analysts assume a higher prepayment rate when the interest rate is at the lower level of the two rates—interest and prepayment. 

Revenue sharing and valuation models promote joint production of mobile services Bandwidth of mobile networks becomes sufficient to provide all demanded services A service can be easily offered via different access channels Consolidation of Incumbent service operators continues... 

---