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Valuation of Financial Derivatives in Discrete-Time Models

Jönsson, Henrik (2013) FMSL01 20131
Mathematical Statistics
Abstract (Swedish)
The core subject of financial mathematics concerns the issue of pricing
financial assets such as complex financial derivatives. The pricing technique
is pervaded by the concept of arbitrage: mis-pricing will be spotted
and exploited, resulting in a risk free return for any arbitrageur. A mispriced
financial asset will expose the issuer to be exploited by the market
as a money-pump.
To prevent arbitrage, when pricing one turns to mathematics. The
no-arbitrage pricing is thus formalized as a mathematical problem and
it is possible to prove a mathematical pricing relationship for a financial
derivative. In some specific cases it is even possible to calculate an explicit
price.
This thesis will consider the pricing technique of a... (More)
The core subject of financial mathematics concerns the issue of pricing
financial assets such as complex financial derivatives. The pricing technique
is pervaded by the concept of arbitrage: mis-pricing will be spotted
and exploited, resulting in a risk free return for any arbitrageur. A mispriced
financial asset will expose the issuer to be exploited by the market
as a money-pump.
To prevent arbitrage, when pricing one turns to mathematics. The
no-arbitrage pricing is thus formalized as a mathematical problem and
it is possible to prove a mathematical pricing relationship for a financial
derivative. In some specific cases it is even possible to calculate an explicit
price.
This thesis will consider the pricing technique of a widely used financial
derivative - the option. Black-Scholes theory is, since its introduction in
1973, the main tool used for option pricing. The theory that derives the
famous Black-Scholes formula involves a great amount of financial and
mathematical theory, however often ignored by the user. This thesis tries
to bring key concepts into light, hopefully leaving the reader (and writer)
with a deeper understanding.
Finance, in general, involves a great amount of uncertainty. To be
able to express this uncertainty in a mathematical manner, one introduces
probability theory. There will be a go-trough of basic probability theory
needed to fully adopt the concept of an equivalent martingale measure
which is the essential tool in arbitrage-free pricing.
By introducing the time-discrete Cox-Ross-Rubinstein model and prove
existence and uniqueness of an equivalent martingale measure, one is able
to state the arbitrage-free price of a European call option. The model is
then compared to the continues-time Black-Scholes model and in conclusion
it is proved and showed that the asymptotic price of the CRR model
is the same as the price calculated by the Black-Scholes formula. (Less)
Please use this url to cite or link to this publication:
author
Jönsson, Henrik
supervisor
organization
course
FMSL01 20131
year
type
M2 - Bachelor Degree
subject
language
English
id
3798724
date added to LUP
2013-05-22 09:24:48
date last changed
2013-05-22 09:24:48
@misc{3798724,
  abstract     = {The core subject of financial mathematics concerns the issue of pricing
financial assets such as complex financial derivatives. The pricing technique
is pervaded by the concept of arbitrage: mis-pricing will be spotted
and exploited, resulting in a risk free return for any arbitrageur. A mispriced
financial asset will expose the issuer to be exploited by the market
as a money-pump.
To prevent arbitrage, when pricing one turns to mathematics. The
no-arbitrage pricing is thus formalized as a mathematical problem and
it is possible to prove a mathematical pricing relationship for a financial
derivative. In some specific cases it is even possible to calculate an explicit
price.
This thesis will consider the pricing technique of a widely used financial
derivative - the option. Black-Scholes theory is, since its introduction in
1973, the main tool used for option pricing. The theory that derives the
famous Black-Scholes formula involves a great amount of financial and
mathematical theory, however often ignored by the user. This thesis tries
to bring key concepts into light, hopefully leaving the reader (and writer)
with a deeper understanding.
Finance, in general, involves a great amount of uncertainty. To be
able to express this uncertainty in a mathematical manner, one introduces
probability theory. There will be a go-trough of basic probability theory
needed to fully adopt the concept of an equivalent martingale measure
which is the essential tool in arbitrage-free pricing.
By introducing the time-discrete Cox-Ross-Rubinstein model and prove
existence and uniqueness of an equivalent martingale measure, one is able
to state the arbitrage-free price of a European call option. The model is
then compared to the continues-time Black-Scholes model and in conclusion
it is proved and showed that the asymptotic price of the CRR model
is the same as the price calculated by the Black-Scholes formula.},
  author       = {Jönsson, Henrik},
  language     = {eng},
  note         = {Student Paper},
  title        = {Valuation of Financial Derivatives in Discrete-Time Models},
  year         = {2013},
}