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Pricing Forward Start Options in Models
Based on (Time-Changed) Lévy Processes
-- Philipp Beyer and Jörg Kienitz
Options depending on the forward skew are very popular. One such option is the forward starting call
option—the basic building block of a cliquet option. The models which are widely applied to account for the
forward skew dynamics, to price such options include the Heston model, Heston-Hull-White model and Bates
model. Within these models, solutions for options including forward start features are available using (semi)
analytical formulas. Now, exponential (subordinated) Lévy models have become increasingly popular for modeling
the asset dynamics. While the simple exponential Lévy models imply the same forward volatility surface for
all future times, the subordinated models do not. Depending on the subordinator the dynamic of the
forward volatility surface and therefore stochastic volatility can be modeled. Analytical pricing formulas based on
the characteristic function and Fourier transform methods are available for this class of models. This
paper extends the applicability of analytical pricing to options including forward start features. To this end,
it derives the forward characteristic functions which can be used in Fourier transform-based methods.
As examples, the paper considers the Variance Gamma (VG) model and the Normal Inverse Gaussian
(NIG) model subordinated by a Gamma-Ornstein-Uhlenbeck process and respectively by a Cox-Ingersoll-Ross
process. The analytical results obtained are also checked by applying the Monte Carlo methods. These results can,
for instance, be applied for calibration of the forward volatility surface. © 2009 IUP. All Rights Reserved.
Airline Hedging Using Derivatives
-- Tumellano Sebehela and Kagiso Madimabe
In volatile economic environment, it is imperative for the airlines to implement appropriate derivative
hedging strategies. In non-volatile economic environment, there seems to be different views that support
non-implementation and implementation of derivative hedging strategies within the non-dominant school
of thought as it can be inferred from Carter et al. (2004). Risk management should take into account
everything that affects the financial positions of the airlines from initial stage to the final one with proper monitoring
in between. While designing a derivative hedging strategy, the risk manager should
take into account all these factors and implement the best possible derivative hedging strategy. © 2009 IUP. All Rights Reserved.
Revisiting the Valuation
of Inflation Indexed Bonds and Derivatives
-- Marco Realdon
This paper presents a tractable model in closed form for pricing inflation indexed bonds, swaps and
options. In keeping with empirical evidence, the model predicts that deflation is unlikely. Various model variants
have been presented in this paper. Inflation may `jump'. Nominal interest rates may be modeled through a
Gaussian model, a quadratic model, etc. Closed-form solutions for inflation indexed bonds, swaps and options
have been presented in both continuous and discrete time settings. In discrete time, the model can be
estimated more easily, the market price of inflation risk can be specified with more freedom, and as in continuous
time, a change of measure provides the closed-form solutions for European type inflation options and options
on nominal bonds. © 2009 IUP. All Rights Reserved.
Valuation of Swaps and Options
on Constant Maturity CDS Spreads
-- Anlong Li
This paper studies the pricing of options whose payoffs are contingent on Constant Maturity Credit
Default Swap (CMCDS) spreads. It extends the convexity adjustment method for Constant Maturity Swap (CMS)
in interest rates by modeling the swap rate and CDS spread either as a single factor (a sum of the two) or as
two factors separately. For the latter, the paper explicitly models the correlation between interest rate and
credit spread in deriving the results. It is shown that when swap rate and CDS spread are independent of each
other and when the yield curve is relatively flat, the two-factor model gives the same convexity adjustment as
the one-factor model. Under lognormality assumptions, the model can produce analytic solutions for
convexity adjustments as well as for the valuation of CMCDS derivatives such as CDS swaptions, caps and floors,
and digital options. © 2009 IUP. All Rights Reserved.
Alternative Assets: A Comparison Between Commodities
and Traditional Asset Classes
-- Claudio Boido and Antonio Fasano
The traditional choice of asset allocation includes stocks, bonds, liquidity and real estate. In the last
five years, as a result of the effects of speculative bubble and the growth of interest rate, the attention of
the managers of the portfolio has shifted to alternative assets, like hedge funds, private equity, credit
derivatives and commodities, to earn extra returns. The commodities, traded on spot and forward markets,
are characterized by the presence of negative correlation with traditional asset classes. Therefore, they
facilitate to obtain a good `alpha', which expresses the non-systematic risk. The commodities have shown
good performance in the last two years, especially the important commodities indices.
Reuters/Jeffries-CRB (Commodities Research Bureau) index and Standard and Poor's Commodity Index (S&P GSCI) have
earned returns over 15%. This paper examines the relationship between the portfolio returns in the presence
of commodities and traditional asset classes (stocks, bonds and liquidity). © 2009 IUP. All Rights Reserved.
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