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A
Lattice Option Pricing Model for Multiple Assets Under Complete
Market Assumption -- Joocheol
Kim and Kyu-Woong Jo
This
study proposes a lattice option pricing model for multiple
underlying assets under the complete market assumption. In
an economy with n-risky assets and a riskless bond, the number
of states can be only (N + 1) to form a dynamically complete
market. Since there are always fewer equations, N means, N
variances plus (N(N - l))/2 correlations than the number of
unknowns, N(N + 1), the nodes cannot be identified uniquely.
This study introduces the concept of rotation in higher dimensional
space to solve the mismatch problem.
©
2008 IUP . All rights reserved.
Interaction
Between Equity and Derivatives Markets in India: An Entropy
Approach -- Y
V Reddy and A Sebastin
The
temporal relationship between the equities market and the
derivatives market segments of the stock market has been studied
using various methods and by identifying lead-lag relationship
between the value of a representative index of the equities
market and the price of a corresponding index futures contract
in the derivatives market. It has been generally observed
that price innovations appear first in the derivatives market
and are then transmitted to the equities market. In this paper,
the dynamics of such information transport between stock market
and derivatives market are studied using the information theoretic
concept of entropy, which captures non-linear dynamic relationship
also.007 IUP . All Rights Reserved.
©
2008 IUP . All Rights Reserved.
Moment
Methods for Exotic Volatility Derivatives -- Claudio
Albanese and Adel Osseiran
The
latest generation of volatility derivatives goes beyond variance
and volatility swaps and probes our ability to price realized
variance and sojourn times along bridges for the underlying
stock price process. In this paper, the authors give an operator
algebraic treatment of this problem, based on Dyson expansions
and moment methods, and discuss applications to exotic volatility
derivatives. The methods are quite flexible and allow for
a specification of the underlying process, which is semiparametric
or even non-parametric, including state-dependent local volatility,
jumps, stochastic volatility and regime switching. The authors
find that particularly volatility derivatives are well suited
to be treated with moment methods, whereby one extrapolates
the distribution of the relevant path functionals on the basis
of a few moments. The authors consider a number of exotics
such as variance knockouts, conditional corridor variance
swaps, gamma swaps and variance swaptions and give valuation
formulas in detail.
©
2008 IUP . All Rights Reserved.
Valuation
of Nifty Options Using Black's Option Pricing Formula -- Subrata
Kumar Mitra
The
Black and Scholes option pricing formula exhibits certain
biases on several parameters used in the model. It has been
observed that the implied volatilities are high for `in-the-money'
options and low for `out-of-the-money' options indicating
that the Black-Scholes model underprices `in-the-money' options
and overprices `out-of-the-money' options. Further, implied
volatility also varies with maturity. In addition to the problems
of changing implied volatility across moneyness and maturity,
Nifty options also suffer from `cost-of-carry' bias, as future
prices of Nifty options are usually less than Nifty spot prices
plus interest element. Since the inception of Nifty future
trading in India, Nifty future even traded below the Nifty
spot value. These deformities obviously cause difference between
the actual price of Nifty options and the prices calculated
using Black-Scholes formula. Black tried to address this problem
of negative cost of carry by using forward prices in the option
pricing model instead of spot prices. He argued that actual
forward prices not only incorporate cost of carry but also
capture various irregularities faced by market forces. In
his model, he replaced the spot price term (S) by the discounted
value of future price (F.e-rt) in the original
Black-Scholes Formula. On the otherhand black's model is widely
used for valuing options on physical commodities as the discounted
value of a quoted future price is found to be a better proxy
of the current spot prices as an input to Black-Scholes formula.
In this study, the theoretical options prices of Nifty options
are calculated using both the Black formula and Black-Scholes
formula, and these theoretical values are compared with the
actual quoted prices in the market. It is found that the Black
formula provides better result in comparison to Black-Scholes
formula for Nifty options.
©
2008 IUP . All Rights Reserved.
Equity
Derivatives in India: Growth Pattern and Trading Volume Effects -- B
S Bodla and Kiran Jindal
Besides
arresting volatility and improving efficiency, the introduction
of derivative contracts in India is aimed at enhancing the
trading volume of stock markets. In view of the above, this
paper is designed to investigate the impact of equity derivatives
on the trading volume of underlying Indian stock market. For
this purpose, the daily traded value data of cash market and
22 individual stocks were collected and analyzed by using
before-and-after control sample technique. The results of
the study show that Compound Annual Growth Rate (CAGR) of
trading volume has declined slightly after the introduction
of derivatives. However, the study found a positive impact
of expiration of derivatives on trading volume of sample stocks.
©
2008 IUP . All Rights Reserved.
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