منابع مشابه
From implied to spot volatilities
Given the quote price of a call or put option, the Black-Scholes implied volatility is the unique volatility parameter to be put into Black-Scholes formula to give the same price as the option quote price. This dissertation is concerned with the link between the implied volatility and the actual volatility of the underlying stock. Such a link is of particular practical interest since it relates...
متن کاملFrom arbitrage to arbitrage-free implied volatilities
We propose a method for determining an arbitrage-free density implied by the Hagan formula. (We use the wording “Hagan formula” as an abbreviation of the Hagan– Kumar–Leśniewski–Woodward model.) Our method is based on the stochastic collocation method. The principle is to determine a few collocation points on the implied survival distribution function and project them onto the polynomial of an ...
متن کاملConvergence of At-the-money Implied Volatilities to the Spot Volatility
We study the convergence of at-the-money implied volatilities to the spot volatility in a general model with a Brownian component and a jump component of finite variation. This result is a consequence of the robustness of the Black–Scholes formula and of the central limit theorem for martingales.
متن کاملImplied and Local Volatilities under Stochastic Volatility
For asset prices that follow stochastic-volatility diffusions, we use asymptotic methods to investigate the behavior of the local volatilities and Black–Scholes volatilities implied by option prices, and to relate this behavior to the parameters of the stochastic volatility process. We also give applications, including risk-premium-based explanations of the biases in some näıve pricing and hedg...
متن کاملImplied Volatilities of Caps: a Gaussian approach
Implied volatilities of interest rate derivatives present some distinctive features, like the inverse relation with the underlying rates and the humped or decreasing shape of their term structure. The objective of this paper is to analyze and explain such features in a Gaussian framework. We will use an approximate relation which separates in a simple and natural way the effects on the implied ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Finance and Stochastics
سال: 2009
ISSN: 0949-2984,1432-1122
DOI: 10.1007/s00780-009-0112-1