Empirical evidence on volatility estimators

Are historical volatilities better then implied volatilities in estimeting future (also kown as actual or realised) volatilities? Which method of measuring historical or implied volatility is best? In this paper we discuss the methodology for calculating these approaches to volatility, carry out empirical tests on each estimator, as well as on their interrelations. In order to test the "quality" of the estimators, comparisons among historical, implied and future volatilities were used for a full range of estimators. This identifies some of the criticisms for each estimator. The differences found among different estimators are statistically significant and should became fully noted by users of volatilities in the pricing and trading "volatility dependent securities" such as options. Moreover we observed some empirical evidence of the so-called "smile effect" that explains why implied volatility estimators that embody the moneyness effect show lower errors in predicting future volatilities. We also found some empirical evidence for the increase of the smile effect with the approach of the maturity. We also found that the selection of a specific estimator can lead to biased conclusions when studying the forecast ability of implied volatilities. Finally the exercise price effect seems to be asymmetrically dependent on stock price changesinfo:eu-repo/semantics/publishedVersio

Numerical solution of a two state variable contingent claims mortgage valuation modelªᵇ

Previously published work on mortgage component valuation has concentrated on the US market and is inapplicable to some of the mortgage arrangements outside of that market. We model UK repayment mortgages with capped Mortgage Insurance Guarantees (which affect both the equilibrium lending rates and the lender's residual exposure). A contingent claims framework is developed, with an explicit finite differences solution. Then the mortgage components are valued, assuming arrangement fees but no prepayment penalties, under various scenarios, and also under equilibrium conditions: The transformation of the original PDE, and the details of the finite difference solution are given, along with graphical sensitivities of the mortgage participants (including the options held or written by the borrower, the insurer, and the lender) to interest rates and house pricesinfo:eu-repo/semantics/publishedVersio

Sequential investments with stage-specific risks and drifts

YesWe provide a generalized analytical methodology for evaluating a real sequential investment opportunity, which does not rely on a multivariate distribution function, but which allows for stage-specific risks and drifts. This model may be a useful capital budgeting and valuation tool for exploration and development projects, where risks change over the stages. We construct a stage threshold pattern whereby the final stage threshold exceeds the early stage threshold due to drift differentials between the project values at the various stages, value volatility differences, and correlation differentials, implying a rich menu of parameter values that may be suitable for a variety of projects. Governments seeking to motivate early final stage investments might lower final stage project volatility or specify project value decline over time, unless prospective owners are willing to pay the real option value (ROV) for concessions. In contrast, concession owners, more interested in ROV than thresholds that motivate early investments, may welcome final stage value escalation, or guarantees that reduce the correlation between project value and construction cost

The effects of an uncertain abandonment value on the investment decision

YesUsing a three-factor stochastic real option model framework, this paper examines the effects of abandonment on the investment decision. Abandonment is classified according to whether the opportunity arises for an active operating asset post-investment, or for holding the project opportunity pre-investment. Separate analytical models are developed for the alternative forms of abandonment optionality. Numerical sensitivity analysis shows that the presence of a post-investment abandonment opportunity makes the investment opportunity appear to be more attractive because of the abandonment option value, but not by a considerable amount. Also, in contrast to the standard real option finding, an abandonment value volatility increase produces a project value threshold fall owing to the increase in the abandonment option value

Rivalry and uncertainty in complementary investments with dynamic market sharing

We study the effects of revenue and investment cost uncertainty, as well non- preemption duopoly competition, on the timing of investments in two complementary inputs, where either spillover-knowledge is allowed or proprietary-knowledge holds. We find that the ex-ante and ex-post revenue market shares play a very important role in firms’ behavior. When competition is considered, the leader’s behavior departs from that of the monopolist firm of Smith (Ind Corp Change 14:639–650, 2005). The leader is justified in following the conventional wisdom (i.e., synchronous investments are more likely), whereas, the follower’s behavior departs from that of the conventional wisdom (i.e., asynchronous investments are more likely)