Submitted by Jayaprakash Rao FT200 Assignment Submitted by Jayaprakash Rao

3 Examples of simulations used in Finance domain

3 Examples of simulations used in Finance domain (slide 1 of 3) Monte Carlo methods for option pricing Monte Carlo option model uses Monte Carlo Methods to calculate the value of an option with multiple sources of uncertainty or with complicated features. Monte Carlo valuation relies on risk neutral valuation. Here the price of the option is it’s discounted expected value. The technique applied is (1) to generate a large number of possible, but random, price paths for the underlying via simulation (2) calculate the associated exercise value (i.e. "payoff") of the option for each path. (3) The payoffs are averaged and (4) discounted to today. This result is the value of the option. Monte Carlo Methods are particularly useful in the valuation of options with multiple sources of uncertainty or with complicated features, which would make them difficult to value through a straightforward Black–Scholes-style or lattice based computation. The technique is thus widely used in valuing path dependent structures like lookback and Asian options and in real options analysis. Additionally, as above, the modeller is not limited as to the probability distribution assumed. https://in.pycon.org/cfp/2016/proposals/financial-modelling-and-simulation-with-python-using-numpy-scipy-matplotlib-and- pandas~b69Qa/?ref=schedule

3 Examples of simulations used in Finance domain (slide 2 of 3) Geometric Brownian motion A geometric Brownian motion (GBM) (also known as exponential Brownian motion) is a continuous-time stochastic process in which the logarithm of the randomly varying quantity follows a Brownian motion (also called a Wiener process) with drift. It is an important example of stochastic processes satisfying a stochastic differential equation (SDE); in particular, it is used in mathematical finance to model stock prices in the Black–Schole model. Geometric Brownian motion is used to model stock prices in the Black–Scholes model and is the most widely used model of stock price behaviour. Some of the arguments for using GBM to model stock prices are: The expected returns of GBM are independent of the value of the process (stock price), which agrees with what we would expect in reality. A GBM process only assumes positive values, just like real stock prices. A GBM process shows the same kind of 'roughness' in its paths as we see in real stock prices. Calculations with GBM processes are relatively easy. However, GBM is not a completely realistic model, in particular it falls short of reality in the following points: In real stock prices, volatility changes over time (possibly stochastically), but in GBM, volatility is assumed constant. In real life, stock prices often show jumps caused by unpredictable events or news, but in GBM, the path is continuous (no discontinuity). https://in.pycon.org/cfp/2016/proposals/financial-modelling-and-simulation-with-python-using-numpy-scipy-matplotlib-and-pandas~b69Qa/?ref=schedule

3 Examples of simulations used in Finance domain (slide 3 of 3) Example 3: Black–Scholes model The Black–Scholes model is a mathematical model of a financial market containing derivative investment instruments. The key idea behind the model is to hedge the option by buying and selling the underlying asset in just the right way and, as a consequence, to eliminate risk. This type of hedging is called "continuously revised delta hedging and is the basis of more complicated hedging strategies such as those engaged in by investment banks and hedge funds. https://in.pycon.org/cfp/2016/proposals/financial-modelling-and-simulation-with-python-using-numpy-scipy-matplotlib-and-pandas~b69Qa/?ref=schedule

3 popular programming languages, their unique features and their suitability criteria

3 popular programming languages, their unique features and their suitability criteria (slide 1 of 3) The three most popular IT languages today are Java, Python and C++. They clean up in the job market, cornering most of the programming job postings. They are the most versatile languages in the world, used nearly everywhere for everything. They have the strongest ecosystems and the largest user communities. 1. Java Java is one of the most popular programming languages, used for building server-side applications to video games and mobile apps. It's also the core foundation for developing Android apps, making it a favorite of many programmers. With its WORA mantra (write once, run anywhere). I Java is designed to be portable and run across multiple software platforms.

3 popular programming languages, their unique features and their suitability criteria (slide 2 of 3) 2. Python Python is a powerful high-level, object-oriented programming language. It has simple easy-to-use syntax, making it the perfect language for someone trying to learn computer programming for the first time. Python is a general-purpose language. It has wide range of applications from Web development (like: Django and Bottle), scientific and mathematical computing (Orange, SymPy, NumPy) to desktop graphical user Interfaces (Pygame, Panda3D). The syntax of the language is clean and length of the code is relatively short. It's fun to work in Python because it allows you to think about the problem rather than focusing on the syntax. Applications of Python include Web Applications, Scientific and Numeric Computing, Creating software Prototypes etc.

3 popular programming languages, their unique features and their suitability criteria (slide 3 of 3) C++ is a general-purpose object-oriented programming (OOP) language. C++ is considered to be an intermediate-level language, as it encapsulates both high- and low-level language features. Initially, the language was called "C with classes" as it had all the properties of the C language with an additional concept of "classes." However, it was renamed C++ in 1983. C++ is one of the most popular languages primarily utilized with system/application software, drivers, client-server applications and embedded firmware. The main highlight of C++ is a collection of predefined classes, which are data types that can be instantiated multiple times.. C++ includes several operators such as comparison, arithmetic, bit manipulation and logical operators. One of the most attractive features of C++ is that it enables the overloading of certain operators such as addition. A few of the essential concepts within the C++ programming language include polymorphism, virtual and friend functions, templates, namespaces and pointers.