scholarly journals An Improved Estimator for Black-Scholes-Merton Implied Volatility

2004 ◽  
Author(s):  
Winfried G. Hallerbach
Keyword(s):  
Implied Volatility ◽  
Black Scholes

A note on the Black-Scholes implied volatility with default risk

2010 ◽  
Vol 2 (3) ◽  
pp. 155-170 ◽  
Author(s):  
Shuichi Ohsaki ◽  
Takaaki Ozeki ◽  
Yuji Umezawa ◽  
Akira Yamazaki
Keyword(s):  
Default Risk ◽  
Implied Volatility ◽  
Black Scholes

Arbitrage Pricing

2019 ◽  
pp. 95-118
Author(s):  
Tomas Björk
Keyword(s):  
Continuous Time ◽  
Implied Volatility ◽  
Futures Contracts ◽  
Martingale Measures ◽  
Bank Account ◽  
No Arbitrage ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Financial Derivative ◽  
Delta Hedging

The chapter starts with a detailed discussion of the bank account in discrete and continuous time. The Black–Scholes model is then introduced, and using the principle of no arbitrage we study the problem of pricing an arbitrary financial derivative within this model. Using the classical delta hedging approach we derive the Black–Scholes PDE for the pricing problem and using Feynman–Kač we also derive the corresponding risk neutral valuation formula and discuss the connection to martingale measures. Some concrete examples are studied in detail and the Black–Scholes formula is derived. We also discuss forward and futures contracts, and we derive the Black-76 futures option formula. We finally discuss the concepts and roles of historic and implied volatility.

MARKOV MARKET MODEL CONSISTENT WITH CAP SMILE

2000 ◽  
Vol 03 (02) ◽  
pp. 161-181 ◽  
Author(s):  
P. BALLAND ◽  
L. P. HUGHSTON
Keyword(s):  
Normal Distribution ◽  
Implied Volatility ◽  
Market Model ◽  
Interest Rate Models ◽  
Market Models ◽  
Forward Measure ◽  
Black Scholes ◽  
Log Normal ◽  
Bermudan Swaptions ◽  
Log Normal Distribution

New interest rate models have emerged recently in which distributional assumptions are made directly on financial observables. In these "Market Models" the Libor rates have a log-normal distribution in the corresponding forward measure, and caps are priced according to the Black–Scholes formula. These models present two disadvantages. First, Libor rates do not in reality have a log-normal distribution since the implied volatility of a cap depends typically on the strike. Second, these models are difficult to use for pricing derivatives other than caps. In this paper, we extend these models to allow for a broader class of Libor rate distributions. In particular, we construct multi-factor Market Models that are consistent with an initial cap smile surface, and have the useful feature of exhibiting Markovian Libor rates. We show that these Markov Market Models can be used relatively easily to price complex Libor derivatives, such as Bermudan swaptions, captions or flexi-caps, by construction of a tree of Libor rates.

An Empirical Research on the Informational Efficiency of Model Free Implied Volatility

2008 ◽  
Vol 16 (2) ◽  
pp. 67-94
Author(s):  
Byung Kun Rhee ◽  
Sang Won Hwang
Keyword(s):  
Implied Volatility ◽  
Realized Volatility ◽  
Informational Efficiency ◽  
Option Prices ◽  
Index Options ◽  
Model Free ◽  
Black Scholes ◽  
Option Pricing Model ◽  
Korean Market ◽  
Better Than

Black-Scholes Imolied volatility (8SIV) has a few drawbacks. One is that the model Is not much successful in fitting the option prices. and It Is n야 guaranteed the model is correct one. Second. the usual tradition in using the BSIV is that only at-the-money Options are used. It is well-known that IV's of In-the-money or Qut-of-the-money ootions are much different from those estimated from near-the-money options. In this regard, a new model is confronted with Korean market data. Brittenxmes and Neuberger (2000) derive a formula for volatility which is a function of option prices‘ Since the formula is derived without using any option pricing model. volatility estimated from the formula is called model-tree implied volatillty (MFIV). MFIV overcomes the two drawbacks of BSIV. Jiang and Tian (2005) show that. with the S&P index Options (SPX), MFIV is suoerlor to historical volatility (HV) or BSIV in forecasting the future volatllity. In KOSPI 200 index options, when the forecasting performances are compared, MFIV is better than any other estimated volatilities. The hypothesis that MFIV contains all informations for realized volatility and the other volatilities are redundant is oot rejected in any cases.

A note on Black–Scholes implied volatility

2006 ◽  
Vol 370 (2) ◽  
pp. 681-688 ◽  
Author(s):  
Jesús Chargoy-Corona ◽  
Carlos Ibarra-Valdez
Keyword(s):  
Implied Volatility ◽  
Black Scholes

AN EXPLICIT IMPLIED VOLATILITY FORMULA

2017 ◽  
Vol 20 (07) ◽  
pp. 1750048 ◽  
Author(s):  
DAN STEFANICA ◽  
RADOŠ RADOIČIĆ
Keyword(s):  
Relative Error ◽  
Implied Volatility ◽  
Black Scholes ◽  
Uniformly Bounded

We show that an explicit approximate implied volatility formula can be obtained from a Black–Scholes formula approximation that is 2% accurate. The relative error of the approximate implied volatility is uniformly bounded for options with any moneyness and with arbitrary large or small option maturities and volatilities, including for long dated options and options on highly volatile underlying assets. For options within a large trading range, such as options with maturity less than five years and implied volatility less than 150%, the error of the approximate implied volatility relative to the Black–Scholes implied volatility is less than 10% points.

ASYMPTOTIC APPROXIMATIONS FOR PRICING DERIVATIVES UNDER MEAN-REVERTING PROCESSES

2016 ◽  
Vol 19 (05) ◽  
pp. 1650030 ◽  
Author(s):  
RICHARD JORDAN ◽  
CHARLES TIER
Keyword(s):  
Interest Rates ◽  
Implied Volatility ◽  
Asymptotic Approximations ◽  
Ray Method ◽  
Interest Rate Derivatives ◽  
Put Options ◽  
Merton Model ◽  
Volatility Model ◽  
Black Scholes ◽  
Efficient Alternative

The problem of fast pricing, hedging, and calibrating of derivatives is considered when the underlying does not follow the standard Black–Scholes–Merton model but rather a mean-reverting and deterministic volatility model. Mean-reverting models are often used for volatility, commodities, and interest-rate derivatives, while the deterministic volatility accounts for the nonconstant implied volatility. Trading desks often use numerical methods for real-time pricing, hedging, and calibration when implementing such models. A more efficient alternative is to use an analytic formula, even if only approximate. A systematic approach is presented, based on the WKB or ray method, to derive asymptotic approximations to the density function that can be used to derive simple formulas for pricing derivatives. Such approximations are usually only valid away from any boundaries, yet for some derivatives the values of the underlying near the boundaries are needed such as when interest rates are very low or for pricing put options. Hence, the ray approximation may not yield acceptable results. A new asymptotic approximation near boundaries is derived, which is shown to be of value for pricing certain derivatives. The results are illustrated by deriving new analytic approximations for European derivatives and their high accuracy is demonstrated numerically.

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