# Classic dynamic delta-gamma hedging in Python

I am trying to run a delta-gamma hedge for a Black-Scholes model in Python.The Euler disceretizatioin of the paths is the simplest possible. I wrote the code below but the PnL looks undesirable and wrong. #install pandas import math import numpy as np import scipy as sp import numpy.random as npr import scipy.stats as scs import... go to Article >

# Is Selling Options Still Worth The Risk?

Is Selling Options Still Worth The Risk? Authored by Dominick Paolini and Patrick Hennessy via IPS Strategic Capital, I learned a long time ago as a young broker on Wall Street that when looking at a potential trade, if the numbers... read more

# Predicting time series using Jump Diffusion model and Neural Networks

I am trying to understand the difference between using Jump diffusion model and Neural Networks or more precisely LSTM to predict time series data regardless what that data contains for example a stock price or withdrawals from ATMs. If I look... read more

# Why does a Bermudan option have a higher implied volatility than its European counterpart?

I get that the premium for an earlier exercise should be higher to compensate the seller but intuitively you would think that the spot has "less room to run" in a potentially shorter period of time (due to a potential earlier exercise compared to... read more

# Swaps: What is the difference between Outright and Spread trading?

I understand in Swaps there are two investing strategies called Outrights and Spreads. Could someone please confirm my understanding of them? I understand an Outright strategy in Swaps refers to investing in an ordinary Swap (i.e, fixed vs... read more

# Duration of forward starting swap

For a spot starting interest rate swap, the modified duration is calculated as the modified duration of the fixed rate leg less the modified duration of the floating leg. Each of these calculations is akin to calculating the duration of a fixed... read more

# Vol surface fitting with 5 degrees of freedom

For an options market making operation I need to be able to build a volatility surface, based on only 5 degrees of freedom, like e.g.: MaxPut, MaxCall, Skew, Curve and At The Money Vol. Is there an existing model or mathematical function, that... read more

# How to gamma hedge and vega hedge an autocallable product?

I am pretty new in quantitative finance, and I am interested by the hedging of autocalls. Could you, please explain which financial products should be traded (specify the way, please) to delta hedge, gamma hedge and vega hedge an autocall? And... read more

# Going from $\mathcal{P}$ to $\mathcal{Q}$

Under $\mathcal{P}$, we have the Heston Model given by: $$ d S_{t}=\mu S_{t} d t+\sqrt{\nu_{t}} S_{t} d W_{t}^{S},\\ d \nu_{t}=\kappa\left(\theta-\nu_{t}\right) d t+\xi \sqrt{\nu_{t}} d W_{t}^{\nu}. $$ Assume I estimated these parameters... read more

# Strict stationarity of GARCH(1,1) process

Consider the following GARCH(1,1) process: $$ \epsilon_t = \sigma_t \eta_t \quad \text{where} \quad (\eta_t) \overset{iid}{\sim} \mathcal{N} (0,1)$$ $$ \sigma_t^2 = \omega + \alpha \epsilon_{t-1}^2 + \beta \sigma_{t-1}^2 \quad \text{where} \quad... read more

# Calculate return for a set of securities downloaded using quantmod

I downloaded adjusted closing price using quantmod for a set of securities. I want to calculate daily/weekly/monthly return for all securities. Usual dailyReturn, weeklyReturn etc not working. What do I need to do? Here is my code. tickers read more

# Outrights & Spreads in Swaps

I understand in Swaps there are two investing strategies called Outrights and Spreads. Could someone please confirm my understanding of them? I understand an Outright strategy in Swaps refers to investing in an ordinary Swap (i.e, fixed vs... read more

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