Taylor's Approximation, Application of Derivates, Partial Differentiation
About the Lecture
The lecture Taylor's Approximation, Application of Derivates, Partial Differentiation by Edu Pristine is from the course ARCHIV Calculus PRM. It contains the following chapters:
- Taylor approximation
- Application of derivatives in finance
- Differentiation involving more than one variables
Author of lecture Taylor's Approximation, Application of Derivates, Partial Differentiation
Edu Pristine
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Excerpts from the accompanying material
... "Application of Derivatives in Finance", Partial Differentiation "Integral ...
... a method of approximating the value of a differential function at a particular point "Applications“ in calculations of value at ris. Determine price of an option as the price of the underlying asset changes over time. Linear first order approximation - Utilizes first order derivative - Uses first two terms of Taylor series - ...
... order. Gives better approximation "Higher order ...
... Taylor second degree approximation ...
... Example - For a call options, a delta of 0.5 means that for every $1 the underlying stock increases, the call option will increase by $0.50. For a put options, a delta of 0.5 means that for every $1 the underlying stock increases, the put option will decrease by $0.50 ...
... When the option is near the money, gamma is largest - Similarly, second derivative of option value with respect to underlying price is called gamma ...
... in the volatility of underlying. When the absolute value of Vega is high, the option value is very sensitive to small changes in volatility. A position in the underlying asset has 0 Vegas ...
... calculus "Optimization" Modified duration of ronds ...
