If you plan to write a covered call option which will expire does traditional option pricing theory apply and, if not, what can replace the Greeks?

The primary goal of option pricing theory is to calculate the probability that an option will be exercised at expiration. These calculations are often summarized using "the Greeks", for example, theta is the expected change in the price of the option associated with a 1-unit change in time. Options can either be traded or held until expiration. If the investor's intention is to write a covered call option which will expire, and is indifferent between whether or not the option is exercised, then option pricing theory in general and the Greeks in particular are not directly relevant to them. Here, we consider the question of what information in fact is important to an investor who writes such a covered call option, and then explore the extent to which an analogy between that investor's analysis and the Greeks can be developed. A case study is presented, and then it is demonstrated that an analogue of theta addresses the same general construct of time value decay. The degree to which the writing of covered calls is an investment strategy versus a speculative strategy is also considered. In conclusion, for an investor who intends to write a covered call option with the intention of allowing it to expire, even though the Greeks are not directly helpful, the principles which underpin their derivation very much are.

Distressed Firm Valuation: A Scenario Discounted Cash Flow Approach

Valuation of a distressed company is a very tricky issue, for which many approaches and methods have been provided by the literature. Unfortunately, many of the more suitable proposals from a theoretical point of view (i.e., those based on option pricing theory, and even integrated with game theory) are very difficult to apply to real cases. To face the many contingencies emerging in a real case valuation, a scenario discounted cash flow (SDCF) model is provided here. The focus is on companies at an advanced stage of distress, where their ability to operate as a going concern is in question, and maintenance or recovery of business continuity requires significant interventions in the firm’s strategic, operational, and financial structure. In this context, SDCF, with a number of arrangements elaborated here, appears useful for valuing assets, debt, and equity – from current or potential new investors – and the interactions between them, which are particularly critical for distressed companies. At the same time, SDCF takes into account the firm’s liquidation option, not only at the valuation date but even after a restructuring plan has been launched. The going-concern value including the liquidation option should be the reference point for judging the suitability of business continuity compared to liquidation. In presenting the model, the key concepts and methodology adopted are set out following a numerical example inspired by a real case.

OPTION PRICING IN MARKETS WITH INFORMED TRADERS

The objective of this paper is to introduce the theory of option pricing for markets with informed traders within the framework of dynamic asset pricing theory. We introduce new models for option pricing for informed traders in complete markets, where we consider traders with information on the stock price direction and stock return mean. The Black–Scholes–Merton option pricing theory is extended for markets with informed traders, where price processes are following continuous-diffusions. By doing so, the discontinuity puzzle in option pricing is resolved. Using market option data, we estimate the implied surface of the probability for a stock upturn, the implied mean stock return surface, and implied trader information intensity surface.

Fractional Riccati Equation and Its Applications to Rough Heston Model

Rough volatility models are popularized by \cite{gatheral2018volatility}, where they have shown that the empirical volatility in the financial market is extremely consistent with rough volatility. Fractional Riccati equation as a part of computation for the characteristic function of rough Heston model is not known in explicit form as of now and therefore, we must rely on numerical methods to obtain a solution. In this paper, we give a short introduction to option pricing theory and an overview of the current advancements on the rough Heston model.

Robert C. Merton and the Science of Finance

Starting with his 1970 doctoral dissertation and continuing to today, Robert C. Merton has revolutionized the theory and practice of finance. In 1997, Merton shared a Nobel Prize in Economics “for a new method to determine the value of derivatives.” His contributions to the science of finance, however, go far beyond that. In this article I describe Merton's main contributions. They include the following: 1. The introduction of continuous-time stochastic models (the Ito calculus) to the theory of household consumption and investment decisions. Merton's technique of dynamic hedging in continuous time provided a bridge between the theoretical complete-markets equilibrium model of Kenneth Arrow and the real world of personal financial planning and management. 2. The derivation of the multifactor Intertemporal Capital Asset Pricing Model (ICAPM). The ICAPM generalizes the single-factor CAPM and explains why that model might fail to properly account for observed market excess returns. It also provides a theory to identify potential forward-looking risk premia for use in factor-based investment strategies. It is therefore both a positive and normative theory. 3. The invention of Contingent Claims Analysis (CCA) as a generalization of option pricing theory. CCA applies the technique of dynamic replication to the valuation and risk management of a wide range of corporate and government liabilities. Merton's CCA model for the valuation and analysis of risky debt is known among scholars and practitioners alike as the Merton Model. 4. The development of financial engineering, which employs CCA to design and produce new financial products. Merton was the first to apply CCA to analyze government guaranty programs such as deposit insurance, and to suggest improvements in the way those programs are managed. He and his students have applied his insights at both the micro and macro policy levels. 5. And finally, the development of a theory of financial intermediation that explains and predicts how financial systems differ across countries and change over time. Merton has applied that theory, called functional and structural finance, to guide the design and regulation of financial systems at the levels of the firm, the industry, and the nation. He has also used it to propose reforms in pensions, sovereign wealth funds, and macrostabilization policy.

Estimation of certain parameters of Black-Scholes model in analysing effectiveness of development investments

The option pricing theory has wide applicability in corporate finance, but it is also increasingly used to analyze the effectiveness of non-financial (material) investments. In traditional investment analysis, a project or a new investment should be accepted only if the returns on the project exceed the hurdle rate; in the context of cash flows and discount rates, this translates into projects with positive net present values (NPV). There is no doubt that it does not take full account of the numerous options that usually relate to developer investment. However, in many cases, the valuation of real options is more difficult than the valuation of options for financial assets. In this paper, we will analyze one of the options, which isembedded in capital budgeting projects - the option to delay a project, especially when a the company has exclusive rights to the project. The value of the option is largely derived from the variance in cash flows – the higher the variance, the higher the value of the project delay option. The variance in the present value of cash flows from the project can be estimated in different ways, however, in the case of non-financial investment projects, these methods are very limited. We are analyzing the possibility of estimating this volatility, taking into account the fact that the forecasted cash flows may show varying volatility in individual years. The paper shows, that by using a probability-based valuation model (using the Crystal Ball techniques) it is possible to incorporate uncertainty into the analysis. The method of presented volatility estimation can be applied by taking into account the randomness of many input data to the project.