Questions tagged [normal]

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2
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1answer
160 views

SABR Normal Volatility when F = K

Looking at the papers Arbitrage free SABR (Hagan) Managing Smile Risk (Hagan) Explicit SABR Calibration through simple expansions (Floch) all 3 papers have similar forms for expression for implied ...
7
votes
1answer
166 views

Basic question on Ito integrals

$Let \space X(t) =\begin{cases} 2, \qquad\text{if} \space 0\le t \le 1 \\ 3, \qquad\text{if} \space 1 < t \le 3 \\ -5, \qquad\text{if}\space 3 < t \le 4 \end{cases} $ or in one forumala $...
0
votes
1answer
124 views

What is the distribution of percentage return in general?

In finance, we often assume that the log-returns $\ln(1+R(t))$ follow a normal distribution. Since $\ln(1+R(t)) \approx R(t)$ when $R(t)$ is small, \begin{equation*} dS/S \sim \text{Normal}. \end{...
1
vote
1answer
802 views

Bachelier option delta = probability of exercise?

Under the Black-Scholes model, the delta of a call option is sometimes interpreted as the probability for the option to end in the money. If I assume that the underlying follows a normal distribution ...
6
votes
4answers
2k views

Downward sloping smile in normal model

We consider an stock price $S$ following a normal model: $dS_t = \sigma dW_t$ We can write this as $\frac{dS_t}{S_t}=\frac{\sigma}{S_t}dW_t$ Hence we can see that $S$ follows a "log-normal" ...