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fixed income - zero-coupon bond and forward rate

I will try a simplified approach: Let $P(t,T)$ represent the price at time t of a zero coupon that pays 1 at time T. If you divide the period between t and T into n sub-intervals, assume $F \left( t;... Read More


How to get the local volatility from IV surface?

You can convert the implied volatility to local volatility using this formula: $\sigma^2 \left(T,y\right)=\frac{\frac{\partial w}{\partial T}}{1 -\frac{ y}{w} \frac{\partial w}{\partial y}+\frac{1}{2... Read More


black scholes - how to calculate implied volatility

Yes. You should use that function to calculate the implied volatility - market convention is to always quote implied volatility using the Black-Scholes model. Traders may execute a trade simply by ag... Read More


Arbitrage opportunity between two call options with strike price \$40, \$30 and cost \$4, \$3 respectively?

No you need to subtract the cost of entering your position as well as the financing costs thereof. In this case you actually receive net \$1 option premiums which yields additional interest at maturi... Read More


Since implied volatility is the standard deviation of returns, why do people treat it as the standard deviation of the price process?

I think there are two questions here. First, this abuse of terminology regrading a) the volatility term in the equation describing the dynamics of the process, $dS=rSdt+\sigma S dW$, which is someti... Read More


bond - Discount factor in Hull-White model

A good advice when it comes to the Hull-White model is to never work with the short rate $r(t)$ directly. It will typically be quite unstable and depend on interpolation on the yield curve. Instead i... Read More


risk - Credit VaR Formula

Here is the excel formula with steps: =NORMSDIST((NORMSINV(0.02)+NORMSINV(0.999)×SQRT(0.1))/SQRT(1−0.1)) =NORMSDIST((−2.054+3.09×SQRT(0.1))/SQRT(1−0.1)) =NORMSDIST(-1.135) =12.8% They keep changing t... Read More


equities - Stock price value as a continuous-time stochastic process

Yes and no. Clearly, stock prices (or prices of any asset) are not observed continuously. This applies to both, the value (price) dimension and the time dimension. This however does not mean that we... Read More


options - Risk Neutral Pricing and the Drift

You can compute expectation of drifted processes as well and derive same pricing formulas,but usually its more complicated (compare derivation of Black Scholes using martinglaes and through PDE. PDE... Read More


black scholes - how does stochastic volatility models generate smiles?

Nevermind, i'm just confusing myself. Now I understand what I misunderstood. The implied volatility surface of a prices of calls generated by a stochastic volatility model will not be constant since... Read More