**Research**

## Published articles

Model-free analysis of real option exercise probability and timing

Kang, Sang Baum, and Pascal Letourneau

This paper investigates the effects of modifying a real option's characteristics on its holding value and optimal exercise decision using quantile-preserving spreads and stochastic dominance. We show that the change in exercise probability and timing depends on the preserved quantile, strike price, time of modification, and modification symmetry, and we significantly generalize previously obtained results to an unspecified underlying process and a general call-like payoff function. Our results offer testable predictions that contribute to the literature on climate finance, real options, and financial options and provide practical guidance for determining how to modify a real option to increase or decrease its exercise probability and timing.

Kang, Sang Baum, and Pascal Letourneau

*Quantitative Finance*This paper investigates the effects of modifying a real option's characteristics on its holding value and optimal exercise decision using quantile-preserving spreads and stochastic dominance. We show that the change in exercise probability and timing depends on the preserved quantile, strike price, time of modification, and modification symmetry, and we significantly generalize previously obtained results to an unspecified underlying process and a general call-like payoff function. Our results offer testable predictions that contribute to the literature on climate finance, real options, and financial options and provide practical guidance for determining how to modify a real option to increase or decrease its exercise probability and timing.

**Simulated Greeks for American Options**

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Letourneau, Pascal, and Lars Stentoft

*Quantitative Finance*

This paper develops a method to estimate price sensitivities, so-called Greeks, for American style options using flexible simulation methods combined with initially dispersed state variables. The asymptotic properties of the estimators are studied, and convergence of the method is established. A 2-stage method is proposed with an adaptive choice of optimal dispersion of state variables, which controls and balances off the bias of the estimates against their variance. Numerical results show that the method compares exceptionally well to existing alternatives, works well for very reasonable choices of dispersion sizes, regressors, and simulated paths, and it is robust to choices of these parameters. We apply the method to models with time varying volatility, demonstrating that there are large differences between estimated Greeks with affine and non-affine models, that Greeks vary significantly through periods of crisis, and that the errors made when using Greeks implied from, e.g., misspecified models with constant volatility can be extremely large.

**An Improved Estimation Method for a Family of GARCH Models**

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Letourneau, Pascal (2019)

*Journal of Derivatives*

This paper proposes an improved estimation and calibration method to a family of GARCH models. The suggested method fixes one parameter such that the unconditional kurtosis of the model matches the sample kurtosis. An empirical analysis using Engle and Ng's (1993) NGARCH(1,1) model shows that the method dominates previous estimation methods on multiple aspects. The optimization problem is simplified and made less sensitive to initial values. The optimization time, both when estimating on historical returns and calibrating on option prices, is reduced by roughly 50%. The in-sample fit is barely affected, while the option pricing, in and out of sample is improved.

**Real Options' Exercise Probability and Timing**

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Kang, Sang Baum, and Pascal Létourneau

*(Working Paper)*

A critical difference between real options and financial options lies in that real option holders, writers, and even external stakeholders can modify the characteristics of real options to increase or decrease its exercise probability. One may adjust the strike price, or the level and risk of the underlying process. Using general quantile-preserving spreads to model risk, this paper shows under which conditions an increase in risk may increase the exercise probability and hasten real option exercise. This paper significantly generalizes previously obtained results. The results are useful to determine an optimally parsimonious modification of a real option to increase or decrease its exercise probability and have policy implications.

**A Real Option Analysis on Retiring Existing Coal-fired Electricity Plants in the United States**

Kang, Sang Baum, Pascal Létourneau, and Steven X. Sala (2018)

*Journal of Energy Markets*

To reduce CO2 emissions from the electricity generation sector, the U.S. introduced the Clean Power Plan (CPP) in 2015. Specifically, building block #2 aimed to replace coal-fired electricity generation with natural gas-fired generation. In 2017, the U.S. federal government decided not to honor the U.N.’s Paris Agreement, and repealed the CPP. In this paper, we study the conditions under which a reasonable green policy by a state encourages the early replacement of existing coal plants with new natural gas plants, as CPP building block #2 suggested. Using a real option model, we calculate the probability that a firm makes an investment decision to retire an existing coal plant and build a new natural gas plant within the next few years. We find that the results critically depend on the remaining useful life of the existing coal plant. When the remaining life is short, government policies do not play a significant role in this asset replacement decision. However, if the remaining useful life is approximately 20+ years, a state government’s green policy does plays a significant role in the plant’s replacement. Because such plants were built during the “coal plant boom” period from 1965 to 1987, our findings are particularly relevant.

**Is it still economic to build a new coal-fired power plant in the U.S.? A real option analysis**

Kang, Sang Baum, Pascal Létourneau, and Steven X. Sala (2018)

*Applied Economics Letters*

In the U.S., virtually no new coal-fired power plants have been built in recent years. Both industry experts and academics seem to believe that no rational firm will build a new coal-fired plant. Will such a trend continue in the future? To provide insights into this question, we investigate the optimal decision of an electricity company with an irreversible and deferrable opportunity to build either a new coal-fired or natural gas-fired power plant as its new base-load resource. According to our real option analysis, the optimal decision depends on the location. In the case of the eastern U.S., it is optimal to choose a natural gas plant if a firm is given a choice among a new natural gas plant, a new coal plant and deferring the investment. However, contrary to the common sentiment in the industry and academia, building a new coal plant in the western U.S. is still more economical than building a new natural gas plant in the absence of emission pricing. Furthermore, introducing carbon pricing to western U.S. states, as California did, can substantially increase the probability that a firm will optimally choose a natural gas plant over a coal plant.

**The Model-Free Equivalence Condition for American Spread Options**

Kang, Sang Baum, and Pascal Létourneau (2017)

*Theoretical Economics Letters,*

*7*(04), 757

A spread option involves the right to obtain the spread between two asset prices at a predefined strike price. This type of derivative security is frequently used in financial markets and academic finance. Furthermore, analysts use the spread option technique for real option modeling purposes. Some spread options are American-type in the sense that an option holder may exercise her option prior to the expiration. In this paper, we propose an equivalence condition for American spread options under which they are not exercised early, and are therefore equivalent to European options. Our theoretical results, developed within a model-free economic setting, suggest that the equivalence conditions documented by previous papers do not hold in a distribution-free environment. Traders , quantitative modelers, and financial programmers in various derivatives markets and the real option modeling area may use our results.

**Investor’s Reaction to the Government Credibility Problem: A Real Option Analysis of Emission Permit Policy Risk.**

Kang, Sang Baum, and Pascal Létourneau (2016)

*Energy Economics,*54: 96-107

In relation to creating a CO2 emission permit market, there are two types of climate change policy risks: 1) It is uncertain whether and when a cap-and-trade system will be implemented; and 2) once a policy is in place, there may be government credibility issues. This paper examines the effect of these policy risks on real option decisions of electric power plant investment. To model both an investment decision and generation flexibility, this study evaluates an exotic compound American option on multiple strips of European spread options through the implementation of least squares Monte-Carlo simulation. Government credibility risk leads to more investment in “less green” resources and induces additional cash flow variation, which increases the average time to investment (value of waiting). However, in an extreme case, government credibility can actually hasten investment because the risk may be more favorable to electric power companies. Furthermore, if emission trading is planned to be implemented in the future (e.g., 2020), and the market believes that the probability of successful implementation is low, firms will build a “less green” plant early to benefit from the period before the green rule is applied..

**Refining the Least Squares Monte Carlo Method by Imposing Structure.**

Létourneau, Pascal, and Lars Stentoft (2014)

*Quantitative Finance*14.3 (2014): 495-507.

The least squares Monte Carlo method of Longstaff and Schwartz (2001) has become a standard numerical method for option pricing with many potential risk factors. An important choice in the method is the number of regressors to use and using too few or too many regressors leads to biased results. This is so particularly when considering multiple risk factors or when simulation is computationally expensive and hence relatively few paths can be used. In this paper we show that by imposing structure in the regression problem we can improve the method by reducing the bias.

## Projects

**Evidence of inflation risk pricing in US stock market**

Pascal Létourneau, Garrett Smith

(Working paper)

This paper studies how investors considers the inflation risk in their stock pricing.

**Efficient valuation of American Options**

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Pascal Létourneau, Lars Stentoft

(Working paper)

This paper proposes an efficient method to simultaneously price and compute hedge ratios of a large portfolio of American options.