# implied-volatility

### implied volatility - B-splines: convexity in IV/Price

No, and this is wrong. The implied vols (from market prices) are actually not necessarily convex but yet may be still arbitrage-free, there are many examples of this for various equities. Furthermore... Read More

### black scholes - Implications of shifting the lognormal model for forward rates from a probability perspective

Let \begin{align} L(t; T, T + \Delta) = \frac{1}{\Delta} \left[ \frac{P(t,T)}{P(t, T+\Delta)} - 1 \right] \end{align} be the forward Libor rate at time $t$ for the period $[T, T+\Delta]$. Consider a... Read More

### black scholes - Interpretation of IV and its use in stock movement prediction

The Bachelier model which assumes that price follows a normal distribution is a correct approximation for the Black-Scholes one for short times t. When time is short it's fine to ignore drift becaus... Read More

### implied volatility - Sensitivity of short-term vs long term options' IV

No. Not really. The term-structure of options IV can change shapes through the year. Sometimes short-term options have a higher IV sometimes long-term options have a higher IV. You can take a look a... Read More

### implied volatility - What is forward moneyness and how to calculate it?

The definition of moneyness is not completely standardized, you can see different definitions in the literature: the simple moneyness is $\frac{S}{K}$ (in some cases you will see $\frac{K}{S}$) the... Read More

### black scholes - Determining the implied volatility for options with bid/ask prices below the intrinsic value

Note that \begin{align} (K-S_T)^+ \ge K-S_T. \end{align} Then \begin{align} p &\equiv E\Big(e^{-rT} (K-S_T)^+ \Big)\\ &\ge E\Big(e^{-rT} (K-S_T) \Big)\\ &=K\, e^{-rT} - S_0\\ &= 670 \times e^{-0.05 \... Read More

### Estimate Beta of CAPM from Implied Volatility?

Yes it is a better way. Just take a look to figure 3, from Buss and Vilkov (2012, RFS):... Read More

### options - What drives changes in implied volatility on ETFs/ETNs?

I'm going to go ahead an assume the spread you were looking at involved exchange traded options. As you presumably know, the actual implied volatility on your screen is a number derived from option p... Read More

### options - How is volatility different from variance?

Let's skip calling it volatility and variance. Let us deal with variance and standard deviation. For normally distributed variables, it is very important to distinguish between the true variance and... Read More

### What is the connection between the risk neutral implied density and the real world density?

I'll outline how you can estimate the (implied) real-world density function from (observed) option prices. Having found this real-world density, you can then compute all sorts of probabilities and qu... Read More