NDLI: Risk-Neutral Pricing in the (B, S) Economy: One Underlying Stock

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Risk-Neutral Pricing in the (B, S) Economy: One Underlying Stock

Content Provider	Scilit
Author	Campolieti, Giuseppe Makarov, Roman N.
Copyright Year	2018
Description	At this point we have the necessary tools in stochastic analysis for developing the theory of derivative pricing and hedging in continuous time in an economy where risky assets are modelled as Itô processes. In this chapter we consider an economy with two securities: a single tradable risky asset, namely, a stock, and a money market (bank) account or a bond. We refer to this as a (B, S) economy with only two tradable assets: B stands for the bank account or bond and S stands for the stock. More specifically, this chapter is devoted to presenting the theoretical framework solely within the classical case of an economy where the interest rate is fixed and the stock price is modelled as a standard geometric Brownian motion (GBM) with constant growth rate and constant volatility. The case in which the stock pays a dividend yield is also included later. The only source of randomness driving the stock price is a single Brownian motion. This is also referred to as the standard Black–Scholes framework. This can be thought of as the continuous-time analogue of the standard binomial tree model which was formally discussed in great detail in Chapter 7. The analogues of the up and down market moves in discrete time are now random movements of the underlying (driving) Brownian motion. The same important underlying concepts of self-financing, replication, hedging, arbitrage, and no-arbitrage pricing of derivative contracts in discrete time now carry over into the continuous-time setting. Book Name: Financial Mathematics
Related Links	https://content.taylorfrancis.com/books/download?dac=C2011-0-08796-5&isbn=9781315373768&doi=10.1201/9781315373768-12&format=pdf
Ending Page	552
Page Count	56
Starting Page	497
DOI	10.1201/9781315373768-12
Language	English
Publisher	Informa UK Limited
Publisher Date	2018-10-24
Access Restriction	Open
Subject Keyword	Book Name: Financial Mathematics
Content Type	Text

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