Author

Baron Law

Date Updated

2022/11/21

Category

q-fin.CP

Date Published

2021/11/11

Date Retrieved

2022/11/22

Description

A simple method is proposed to estimate the instantaneous correlations
between state variables in a hybrid system from the empirical correlations
between observable market quantities such as spot rate, stock price and implied
volatility. The new algorithm is extremely fast since only low-dimension linear
systems are involved. If the resulting matrix from the linear systems is not
positive semidefinite, the shrinking method, which requires only
bisection-style iterations, is recommended to convert the matrix to positive
semidefinite. The square of short-term at-the-money implied volatility is
suggested as the proxy for the unobservable stochastic variance. When the
implied volatility is not available, a simple trick is provided to fill in the
missing correlations. Numerical study shows that the estimates are reasonably
accurate, when using more than 1,000 data points. In addition, the algorithm is
robust to misspecified interest rate model parameters and the
short-sampling-period assumption. G2++ and Heston are used for illustration but
the method can be extended to other affine term structure, local volatility and
jump diffusion models, with or without stochastic interest rate.

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URL

https://arxiv.org/abs/2111.06042

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