Pricing options considering liquidity factor

<p>The purpose of the thesis is to study the impact of the illiquid market of the underlying asset on options pricing. Relevance of the topic is related to the specification of derivatives and their large trading volumes around the world. Also, in my opinion, there is limited number of articles on the problem.</p><p>The object of this thesis is stock options. The subject of the presented work is to study the pricing of derivatives considering limited liquidity of the underlying asset.</p><p>The goal of the thesis is to construct a theoretical model for determining the price of option contract. Also, we study the influence of liquidity parameters describing market of the underlying asset ​​by introducing the supply curve setting dependence between price of transaction and its size.</p><p>To achieve this aim the following tasks has been implemented:</p><p>1. To conduct a review and systematize existing literature on the subject;</p><p>2. To select the projection of market liquidity, which is best suited for studying the formulated problem;</p><p>3. To construct theoretical model that describes pricing of options based on constrained market liquidity of the underlying asset;</p><p>4. To check hypothesis about existence of the supply curve for a number of securities trading at Russian market;</p><p>5. To formulate a method for determining the value of the option;</p><p>6. To perform valuation of European call option for the specified parameters;</p><p>7. To formulate conclusions obtained in the work and compare them with the results of other authors.</p><p>In this study we apply logical methods, econometric theory and method of dynamic programming for deciding specified tasks.</p><p>The main points of scientific newness of this study include modification of existing models related to the formulated subject of research; application of known methods to the new domain, which allows receiving new knowledge about the studied object.</p><p>To construct a theoretical model we use the supply curve for the underlying asset, which has a different type in case of buying and selling stocks. In addition, it takes into account the existence of bid-ask spread in the market of the investigated asset. This paper presents an algorithm for determining the value of an option contract under these conditions; we also check formulated method for the specific values of variables. It is shown that limited liquidity of shares reflected in the growth of the option premium for this asset.</p><p>Special attention is paid to the study of the existence of the supply curve in formulated in the Russian securities market. We check this assumption by using per-minute book data on ordinary shares of OJSC &quot;Gazprom&quot;, &quot;Sberbank of Russia&quot; and NK &quot;Rosneft&quot; from 10:00 to 18:39 for the period from April 22 to April 25, 2014. For selected assets has been shown that it is possible to argue that assumption of the specified supply curve form is right and for these assets we can talk about existing of a discontinuous function describing the dependence of the transaction price from its volume.</p><p>These results confirm the findings from previous works on option pricing problems due to the limited liquidity of the underlying asset and indicate the importance of taking them into account in practice.</p>