Dean Paxson

Developing real option game models

By mixing concepts from both game theoretic analysis and real options theory, an investment decision in a competitive market can be seen as a “game” between firms, as firms implicitly take into account other firms’ reactions to their own investment actions. We review two decades of real option game models, suggesting which critical problems have been “solved” by considering game theory, and which significant problems have not been yet adequately addressed. We provide some insights on the plausible empirical applications, or shortfalls in applications to date, and suggest some promising avenues for future research.

Persistence in Portuguese mutual fund performance

Recent evidence suggests that future performance is predictable from past performance, that is, funds with superior (inferior) performance in the past are likely to remain good (bad) performers in the future. This research addresses the persistence of mutual fund performance in a European regional market (the Portuguese equity fund market). Some of the problems in evaluating fund persistence are identified in the context of limited sample size and using the peer group median as a benchmark for contingency table analysis of performance persistence. The criteria for assessing performance persistence based on the contingency table methodology of repeated winners and losers are presented in terms of significance statistics, adjusted for small sample bias. The adjustments are accomplished through the Yates continuity correction and Fishers exact p-value. The appropriateness of each criteria under different circumstances is also discussed. The analysis of the returns of all Portuguese domestic equity funds, since a representative number was established, shows some performance persistence (on a quarterly basis). The persistence, however, is reduced when the returns are controlled for the various dimensions of risk. Significant risk persistence has been documented. Furthermore, for more or less frequent intervals of measurement, the industry persistence is rejected, although individual funds exhibit superior/inferior performance.

Renewing Assets with Uncertain Revenues and Operating Costs

We study optimal replacement and abandonment decisions for real assets, when both revenues and costs are uncertain and deteriorate with age. We develop an implicit representation of the renewal boundary as the solution to a set of simultaneous equations. This quasi-analytical method has the merit of computational ease and transparency. We show that the correlation between revenues and operating costs has a significant influence on the renewal boundary, and that the increase in revenue immediately following a renewal has a greater relative influence on the boundary than either operating cost or renewal cost. The quasi-analytical method is sufficiently flexible to deal with other real option models involving 2 variables.

UK Fixed Rate Repayment Mortgage and Mortgage Indemnity Valuation

We use a mean-reverting interest rate model and a lognormal house price diffusion model to evaluate British fixed rate repayment mortgage contracts with (embedded) default and prepayment options. The model also provides values for capped mortgage indemnity guarantees and the corresponding (residual) lenders coinsurance. Since the partial differential equation incorporating the general features of these mortgage contracts does not have a closed-form solution, an explicit finite difference method is used for the valuation (and sensitivity) results, with solution improvements to deal with error bounds. Then we provide graphical representations of each mortgage component as a function of house prices and interest rate levels, along with interpretations of the analysis. We calculate precisely the lenders (residual) exposure to house price risk, given the borrowers options, house and interest rate uncertainty, and customary mortgage indemnity insurance for high loan/collateral ratio mortgages. Copyright 2002 by the American Real Estate and Urban Economics Association.

Subsidies for Renewable Energy Facilities Under Uncertainty

We derive the optimal investment timing and real option value for a facility with price and quantity uncertainty, where there might be a government subsidy proportional to production quantity. Where the subsidy is proportional to the multiplication of the price and quantity, dimensionality can be reduced. Alternatively, we provide quasi‐analytical solutions for different quantity subsidy arrangements: permanent (policy is certain); retractable; suddenly permanent; and suddenly retractable. Whether policy uncertainty acts as a disincentive for early investment depends on the type of subsidy arrangement. The greatest incentive for early investment is an actual retractable subsidy, a ‘flighty bird in hand’.

Confined exponential approximations for the valuation of American options

We provide an alternative analytic approximation for the value of an American option using a confined exponential distribution with tight upper bounds. This is an extension of the Geske and Johnson compound option approach and the Ho et al. exponential extrapolation method. Use of a perpetual American put value, and then a European put with high input volatility is suggested in order to provide a tighter upper bound for an American put price than simply the exercise price. Numerical results show that the new method not only overcomes the deficiencies in existing two-point extrapolation methods for long-term options but also further improves pricing accuracy for short-term options, which may substitute adequately for numerical solutions. As an extension, an analytic approximation is presented for a two-factor American call option.

Leader/Follower Real Value Functions if Market Share Follows a Birth/Death Process

Publisher Summary In a duopoly setting where one of the firms is the first to enter, defined as the leader, and the other one is the follower. There are some advantages and disadvantages for assuming either of the roles. The leader normally has advantages in distribution, product line breadth, product line, and market share. The follower can have lower adoption costs and a reduction in uncertainty, through learning from the leaders mistakes. An adequate model to determine investment/entry timing should consider the strategic policies of each firm and consequently include the advantages and disadvantages of each role. More than 70% of current market leaders are market pioneers. Although being first does not necessarily induce an advantage, it certainly creates an opportunity. When the pioneer is alone in the market, the leader enjoys the revenues of a monopolist; when other firms enter, the pioneer can continue to be the leader or not and that depends on his or her ability to satisfy customers and innovate.

Continuous rainbow options on commodity outputs: what is the real value of switching facilities?

We develop real rainbow option models to value an operating asset with the flexibility to choose between two commodity outputs. We provide a quasi-analytical solution and a numerical lattice solution to a model with continuous switching opportunities between two commodity outputs, taking into account operating and switching costs. The models are applied to an illustrative case, demonstrating that the quasi-analytical solution and the lattice approach provide near identical results for the asset valuation and optimal switching boundaries. We find that the switching boundaries generally narrow as prices decline. In the presence of operating costs and temporary suspension, however, the thresholds diverge for low enough prices. A fertilizer plant with flexibility between selling ammonia and urea is valued in an empirical section using our real option models. Despite the high correlation between the two alternative commodities, ammonia and urea, there is significant value in the flexibility to choose between the two. Both strategic and policy implications for stakeholders in flexible assets are discussed, with some generalisations outside the fertilizer industry.

Replacement decisions with multiple stochastic values and depreciation

We develop an analytical real-option solution to the after-tax optimal timing boundary for a replaceable asset whose operating cost and salvage value deteriorate stochastically. We construct a general replacement model, from which seven other particular models can be derived, along with deterministic versions. We show that the presence of salvage value and tax depreciation significantly lowers the operating cost threshold that justifies (and thus hastens) replacement. Although operating cost volatility increases defer replacement, increases in the salvage value volatility hasten replacement, albeit modestly, while increases in the correlation between costs and salvage value defer replacement. Reducing the tax rate or depreciation lifetime, or allowing an investment tax credit, yield mixed results. These results are also compared with those of less complete models, and deterministic versions, showing that failure to consider several stochastic variables and taxation in the replacement process may lead to sub-optimal decisions.

Modelling the number of customers as a birth and death process

Birth and death may be a better model than Brownian motion for many physical processes, which real options models will increasingly need to deal with. In this paper, we value a perpetual American call option, which gives the monopoly right to invest in a market in which the number of active customers (and hence the sales rate) follows a birth and death process. The problem contains a singular point, and we develop a mixed analytic/numeric method for handling this singular point, based on the method of Frobenius. The method may be useful for other cases of singular points. The birth and death model gives lower option values than the geometric Brownian motion model, except at very low volatilities, so that if a firm incorrectly assumes a geometric Brownian motion process in place of a birth and death process, it will invest too seldom and too late.