Valuation of Financial Derivatives in DiscreteTime Models
(2013) FMSL01 20131Mathematical 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: mispricing 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 moneypump.
To prevent arbitrage, when pricing one turns to mathematics. The
noarbitrage 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: mispricing 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 moneypump.
To prevent arbitrage, when pricing one turns to mathematics. The
noarbitrage 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. BlackScholes theory is, since its introduction in
1973, the main tool used for option pricing. The theory that derives the
famous BlackScholes 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 gotrough of basic probability theory
needed to fully adopt the concept of an equivalent martingale measure
which is the essential tool in arbitragefree pricing.
By introducing the timediscrete CoxRossRubinstein model and prove
existence and uniqueness of an equivalent martingale measure, one is able
to state the arbitragefree price of a European call option. The model is
then compared to the continuestime BlackScholes 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 BlackScholes formula. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/studentpapers/record/3798724
 author
 Jönsson, Henrik
 supervisor

 Nader Tajvidi ^{LU}
 organization
 course
 FMSL01 20131
 year
 2013
 type
 M2  Bachelor Degree
 subject
 language
 English
 id
 3798724
 date added to LUP
 20130522 09:24:48
 date last changed
 20130522 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: mispricing 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 moneypump. To prevent arbitrage, when pricing one turns to mathematics. The noarbitrage 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. BlackScholes theory is, since its introduction in 1973, the main tool used for option pricing. The theory that derives the famous BlackScholes 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 gotrough of basic probability theory needed to fully adopt the concept of an equivalent martingale measure which is the essential tool in arbitragefree pricing. By introducing the timediscrete CoxRossRubinstein model and prove existence and uniqueness of an equivalent martingale measure, one is able to state the arbitragefree price of a European call option. The model is then compared to the continuestime BlackScholes 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 BlackScholes formula.}, author = {Jönsson, Henrik}, language = {eng}, note = {Student Paper}, title = {Valuation of Financial Derivatives in DiscreteTime Models}, year = {2013}, }