American options with stochastic dividends and volatility: A nonparametric investigation

TLDR: In this paper, the authors provide a full discussion of the theoretical foundations of American option valuation and exercise boundaries and show how they depend on the various sources of uncertainty which drive dividend rates and volatility, and derive equilibrium asset prices, derivative prices and optimal exercise boundaries in a general equilibrium model.

About: This article is published in Journal of Econometrics.The article was published on 2000-01-01 and is currently open access. It has received 95 citations till now. The article focuses on the topics: Implied volatility & Volatility smile.

Figures

Figure 1: Estimated call prices conditional on dividend and EGARCH volatility quartiles. | : rst quartile; { { : second quartile; : third quartile; : fourth quartile.

Figure 2: Estimated call prices conditional on dividend and implied volatility quartiles. | : rst quartile; { { : second quartile; : third quartile; : fourth quartile.

Table 2: Empirical quantiles of ltered conditional variances (̂2)

Figure 3: Estimated exercise boundary as a function of implied volatility.

Table 3: Goodness of t test statistics.

Table 4: American call option normalized prices (C=K).

Frequently asked questions

Q1. What contributions have the authors mentioned in the paper "American options with stochastic dividends and volatility: a nonparametric investigation" ?

In this paper, the authors study the effect of volatility on the performance of the OEX contract on the S & P100 stock index. 

Q2. What procedure was used to choose the bandwith parameter?

To choose the bandwith parameter the authors followed a procedure called generalized cross-validation, described in Craven and Wahba (1979) and used in the context of option pricing in Broadie et. al. (1995). 

Q3. What are the two critical assumptions used in the American option case?

1Two critical assumptions, namely (1) a constant dividend rate and(2) constant volatility, are often cited as restrictive and counter-factual. 

Q4. What is the main goal of the nonparametric approach?

the nonparametric approach does achieve the main goal of their econometric anaylsis, namely to determine whether the volatility and/or the dividend rate a ect the valuation of the contract and the exercise policy. 

Q5. What is the widely used kernel estimator of g in 3.1?

The most widely used kernel estimator of g in (3.11) is the NadarayaWatson estimator de ned byĝ (z) =Pn i=1K Zi zYiPni=1K Zi z ; (3.12) so thatĝ (Z1); : : : ; ĝ (Zn) 0 =WKn ( )Y; where Y = (Y1; : : : ; Yn) 0 and WKn is a n n matrix with its (i; j)-th element equal to K Zj Zi Pn k=1K Zk Zi : WKn is called the in uence matrix associated with the kernel K: 

Q6. What is the argument for the EGARCH volatilities?

The argument is that for a wide variety of misspeci ed ARCH models the di erence between the (EG)ARCH volatility estimates and the true underlying di usion volatilities converges to zero in probability as the length of the sampling time interval goes to zero at an appropriate rate. 

Q7. What papers were devoted to the subject?

Several papers were devoted to the subject, namely Nelson (1990, 1991, 1992, 1996a,b) and Nelson and Foster (1994, 1995), which brought together two approaches, ARCH and continuous time SV, for modelling time-varying volatility in nancial markets. 

Q8. What is the value of a contingent claim?

In this context, the value ofany contingent claim is simply given by its shadow price, i.e., the priceat which the representative agent is content to forgo holding the asset. 

Q9. What are the state variables required to model a stochastic dividend yield?

Two state variables are required tomodel a stochastic dividend yield which is imperfectly correlated with thevolatility coe cients of the stock price process. 

Q10. What is the simplest explanation for the volatility of options?

The results so far seem to suggest two things: (1) conditioning on t does not displace pricing of options and (2) the volatility e ect seems to be present only for large (fourth quartile) volatilities.