Modeling the steel price for valuation of real options and scenario simulation

Abstract

Steel is widely used in construction. I tried to model the steel price such that valuations and scenario simulations could be done. To achieve a high level of precision this is done with a continuous-time continuous-state model. The model is more precise than a binomial tree, but not more economically interesting. I have treated the nearest futures price as the steel price. If one considers options expiring at the same time as the futures, it will be the same as if the spot were traded. If the maturity is short such that details like this matters, one should treat the futures as a spot providing a convenience yield equal to the interest rate earned on the delayed payment. This will in the model be the risk-free rate. Then I have considered how the drift can be modelled for real world scenario simulation. It involves discretion, as opposed to finding a convenient AR(1) representation, because the ADF-test could not reject non-stationarity (unit root). Given that the underlying is traded in a well functioning market such that prices reflect investors attitude towards risk, will the drift of the underlying disappear in the one-factor model applied to value a real-option. The most important parameter for the valuation of options is the volatility. I have estimated relative and absolute volatility. The benefit of the relative volatility is the non-negativity feature. Then I have estimated a model where the convenience yield is stochastic. This has implications for the risk-adjusted model. I have difficulties arriving at reliable parameter estimates. Here small changes in arguments have large effects on the option value. Therefore should this modelling be carried through only if one feels comfortable that it is done properly. I finish by illustrating how real-option valuation can be performed. The trick is to translate the real-world setting into a payoff function. Then one can consider Monte Carlo simulation if the payoff function turns out to be complicated or if there are decisions to be made during the life of the project. For projects maturing within the horizon traded at the exchange, the expectation of the spot price under the pricing measure is observable. To truly compare models, plots of the value of derivative should be created to graphically compare the difference in dependence on parameter values. Alternatively, the derivative of the expressions with respect to the parameters are compared. The value of the option to do something, as opposed to be committed to do something, increases with the volatility of future outcomes. Such known results are used instead in the comparison, because the two reliable models (the one-factor models) are pretty similar. This known result is not contradicted by the present values computed in the real option example.