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The development of standardized measures of institution‐wide volatility exposures has so far lagged that for measures of asset price and interest‐rate exposure—largely because it is difficult to reconcile the various mathematical models used to value options. Recent mathematical results, however, can be used to construct standardized measures of volatility exposure. We consider here techniques for reconciling “vegas” for financial options valued using stochastic models that may be mathematically inconsistent with each other.

How do stock prices evolve over time? The standard assumption of geometric Brownian motion, questionable as it has been right along, is even more doubtful in light of the recent stock market crash and the subsequent prices of U.S. index options. With the development of rich and deep markets in these options, it is now possible to use options prices to make inferences about the risk-neutral stochastic process governing the underlying index. We compare the ability of models including Black–Scholes, naïve volatility smile predictions of traders, constant elasticity of variance, displaced diffusion, jump diffusion, stochastic volatility, and implied binomial trees to explain otherwise identical observed option prices that differ by strike prices, times-to-expiration, or times. The latter amounts to examining predictions of future implied volatilities.

Certain naïve predictive models used by traders seem to perform best, although some academic models are not far behind. We find that the better-performing models all incorporate the negative correlation between index level and volatility. Further improvements to the models seem to require predicting the future at-the-money implied volatility. However, an “efficient markets result” makes these forecasts difficult, and improvements to the option-pricing models might then be limited.

Using volatility cones as the estimate of actual volatility instead of GARCH models, the purpose of this paper is to explore whether volatility arbitrage strategy can provide positive profits and how the transaction costs existed in the real market affect the effectiveness of volatility arbitrage strategy.

A number of hedging approaches proposed to improve the hedging results and final returns of Black-Scholes model are analyzed and compared.

The general finding is that volatility arbitrage strategy can provide satisfactory returns based on the samples in Chinese market. Regarding transaction costs, the variable bandwidth delta and delta tolerance approach showed better results. Besides, choosing futures together with ETFs as hedging underlying can increase the VaR for better risk management.

This paper offers a new method for volatility arbitrage in Chinese financial market.

This paper researches the profitability of the volatility arbitrage strategy on ETF 50 options using volatility cones method for the first time. This method has advantage over the point-wise estimation such as GARCH model and stochastic volatility model.

The purpose of this paper is to develop an option pricing model applicable to US options. The lognormality assumption that has typically been imposed with past binomial and trinomial option pricing models is relaxed. The relaxed lattice model is then used to determine skewness and kurtosis of distributions of futures prices implied from option prices.

The relaxed lattice is based on Gaussian quadrature. The markets studied include corn, soybeans, and wheat. Skewness and kurtosis are implied by minimizing the squared deviations of actual option premia from predicted premia.

Positive skewness is the major source of nonnormality, but both skewness and kurtosis are important as the trinomial model that considers kurtosis has greater accuracy than the binomial model. The out‐of‐sample forecasting accuracy of the relaxed lattice models is better than the Black‐Scholes model in most, but not all cases.

The model might benefit from using option prices from more than one day. The implied skewness and kurtosis were quite variable and using more data might reduce this variability.

Empirical results mostly show positive implied skewness, which suggests extreme price rises were more likely than extreme price decreases.

The relaxed lattice is a new model and the results about implied higher moments are new for these commodities. There are competing models available that should be able to get similar accuracy, so one key advantage of the new approach is its simplicity and ease of use.

Recent developments in accounting for stock options have increased interest in the analytical techniques used to value them. Techniques used to value the options of publicly traded companies have been extensively discussed. In contrast, there has been almost no discussion of the valuation procedures of the options for non‐publicly traded companies. This paper addresses this gap. The paper suggests that a straightforward income capitalization model can be used to develop reasonable surrogates for the variables of the Black‐Scholes option pricing model. The paper also discusses how to adjust the income apitalization model for both lack of marketability and lack of control discounts.

This paper provides a structural model to value startup companies and determine the optimal level of research and development (R&D) spending by these companies.

This paper describes a new variant of float-the-money options, which can act as a financial instrument for financing R&D expenses for a specific time horizon or development stage, allowing the investor to share in the startup's value appreciation over that duration. Another innovation of this paper is that it develops a structural model for evaluating optimal level of R&D spending over a given time horizon. The paper deploys the Gompertz-Cox model for the R&D project outcomes, which facilitates investigation of how increased level of R&D input can enhance the company's value growth.

The author first introduces a time-varying drift term into standard Black-Scholes model to account for the varying growth rates of the startup at different stages, and the author interprets venture capital's investment in the startup as a “float-the-money” option. The author then incorporates the probabilities of startup failures at multiple stages into their financial valuation. The author gets a closed-form pricing formula for the contingent option of value appreciation. Finally, the author utilizes Cox proportional hazards model to analyze the optimal level of R&D input that maximizes the return on investment.

The integrated contingent claims model links the change in the financial valuation of startups with the incremental R&D spending. The Gompertz-Cox contingency model for R&D success rate is used to quantify the optimal level of R&D input. This model assumption may be simplistic, but nevertheless illustrative.

Once supplemented with actual transaction data, the model can serve as a reference benchmark valuation of new project deals and previously invested projects seeking exit.

The integrated structural model can potentially have much wider applications beyond valuation of startup companies. For instance, in valuing a company's risk management, the level of R&D spending in the model can be replaced by the company's budget for risk management. As another promising application, in evaluating a country's economic growth rate in the face of rising climate risks, the level of R&D spending in this paper can be replaced by a country's investment in addressing climate risks.

This paper is the first to develop an integrated valuation model for startups by combining the real-world R&D project contingencies with risk-neutral valuation of the potential payoffs.

The purpose of this article is to propose a detailed methodology to estimate, model and incorporate the non-constant volatility onto a numerical tree scheme, to evaluate a real option, using a quadrinomial multiplicative recombination.

This article uses the multiplicative quadrinomial tree numerical method with non-constant volatility, based on stochastic differential equations of the GARCH-diffusion type to value real options when the volatility is stochastic.

Findings showed that in the proposed method with volatility tends to zero, the multiplicative binomial traditional method is a particular case, and results are comparable between these methodologies, as well as to the exact solution offered by the Black–Scholes model.

The originality of this paper lies in try to model the implicit (conditional) market volatility to assess, based on that, a real option using a quadrinomial tree, including into this valuation the stochastic volatility of the underlying asset. The main contribution is the formal derivation of a risk-neutral valuation as well as the market risk premium associated with volatility, verifying this condition via numerical test on simulated and real data, showing that our proposal is consistent with Black and Scholes formula and multiplicative binomial trees method.

Motivated by recent congressional interest in eradicating government sponsored enterprises (GSE), the purpose of this paper is to develop a framework to price the implicit government guarantee embedded in the bonds issued by the Farm Credit System.

The paper uses the Black‐Scholes model to extract the implied volatilities of the guarantee and then substitute into the model the volatility in historical land prices. The model is developed along the lines of Merton's bond pricing formulation of implicit calls and puts on bond yield risk and default.

Bottom line results show that the average bond yield for a 3M Farm Credit bond from January 13th 2009 to February 10th 2011 would be 0.3744 percent if the Farm Credit System had no GSE status, which is 13.62 bps higher than the actual bond yield. The difference between the hypothetical yield and the actual yield increases with increasing maturity and reaches its peak with 10Y bond where the difference between the hypothetical yield and the actual yield is 68.81 bps. The paper concludes that given the current state of the agricultural credit market in the USA that loss of GSE status and the implied guarantee of Farm Credit bonds would have a minimal effect on short term notes, with a more substantive increase in longer term yields.

The GSE status of the Farm Credit System is an important political issue. This paper provides first estimates of what impact might result from its loss of GSE status. The methods employed are consistent with current models of bond pricing and the results are of direct relevance to Farm Credit System regulators and congressional discussions.

Farm credit is important, if the Farm Credit System loses its GSE status this might affect the competitive balance between commercial and system lenders.

This paper uses option price theory based upon the spread between farm credit bonds and treasury. The approach used requires daily data, but not all attributes of bonds are known. Nonetheless, the results show remarkable consistency for a problem that is largely understudied. There is a need for policy makers, including the US congress to understand the value of government guarantees whether implicit or explicit.

The purpose of this paper is to evaluate Alberta’s cattle loan guarantee program. It measures the risk premiums on lending that would accrue to banks participating in the program, estimates the value (price) of the loan guarantee, and estimates the interest subsidy provided by the program.

A cash flow model of cattle feeding is used. The model estimates a measure of risk that is applied to option pricing models to estimate the value of the guarantee.

Insurance premiums for the credit risk to lenders are 0.20 percent of the value of the loan for the entire feeding period, and 0.41 percent for backgrounding but negligible for finishing. The price of the loan guarantee estimated by the Black-Scholes model is 4.43 percent of the value of the loan and is comparable to prices estimated by the binomial model. The program provides a subsidy rate of 4.58 percent.

Charging a guarantee fee can potentially eliminate the interest subsidy inherent in the program. But this would necessitate determining the impact of the guarantee fee on the additional access to credit that has been achieved through the program.

Different levels of risk for backgrounding and finishing imply different risk premiums on cattle loans. Therefore interest on cattle loans should reflect not only the individual farmer’s risk profile but also the nature of the feeding operation.

This is the first paper to simultaneously estimate risk premiums on cattle feeding loans, the value of the loan guarantee provided by the Alberta Feeder Association Loan Guarantee Program, and the inherent interest subsidy.

On May 18, 2014, AT&T Inc., the second-biggest U.S. mobile-phone carrier, agreed to acquire DirecTV, a satellite-television company, for $49 billion in cash and stock. However, the merger’s conditions and terms are complicated as the stock exchange ratio is contingent on the volume-weighted average AT&T stock price over a 30-day period that is three trading days prior to the date when the merger becomes effective.

Using a contingent claims pricing approach, we model DirecTV’s theoretical value based on the merger’s conditions and terms. It is shown that the theoretical DirecTV stock value is analogous to the sum of the present value of a cash offer, plus owning shares of the AT&T stock, and short volume-weighted average price (VWAP) call spreads. Using three different option-pricing models, DirecTV’s stock valuation model is tested with the market data. Empirical results show that on average, DirecTV’s stock was consistently priced at a discount during the sample period, and Funahashi and Kijima’s (2017) VWAP option model works better than Black and Scholes’ (1973) plain vanilla option model and Levy’s (1992) average-price option model.