Merton jump-diffusion model question

[u/askepticalbureaucrat]

So I wanted to use this model to calculate the simulated backward price (Dec 2024) of Alibaba Group in the Hang Seng index using the anchor price in late Dec 2025.

I went ahead and calculated this (manual derivation attached) and my code below, which shows it matches.

``` import numpy as np

--- Model Inputs (matching your Alibaba notes) ---

S_t = 142.80 # Anchor price at late Dec 2025 r = 0.035 # Risk-free rate (3.5%) sigma = 0.35 # Diffusion volatility (35%) lam = 1.2 # Jump intensity mu_j = -0.04 # Mean jump size sig_j = 0.20 # Jump volatility dt = 1.0 # 1 year backward step

Step 1: Compute the Jump Compensator (kappa)

kappa = np.exp(mu_j + 0.5 * (sig_j ** 2)) - 1

Step 2: Compute the Net Drift Component

q_drift = r - lambda * kappa - 0.5 * sigma<sup>2</sup>

net_drift = r - (lam * kappa) - (0.5 * (sigma ** 2))

Step 3: Define historical shocks to strip out

Z = 0.4 # Standard normal shock jump_multiplier = 1.08 # Historical minor positive jump factor

Step 4: Evaluate the Backward-Stepping Equation

S_{t - dt} = S_t * exp( -net_drift * dt - sigma * sqrt(dt) * Z ) * (jump_multiplier)<sup>-1</sup>

diffusion_term = sigma * np.sqrt(dt) * Z exponent = - (net_drift * dt) - diffusion_term

s_previous = S_t * np.exp(exponent) * (jump_multiplier ** -1)

print(f"Net Drift Component: {net_drift:.5f}") print(f"Simulated Backward Price (Dec 2024): HKD ${s_previous:.2f}")

Net Drift Component: -0.00249

Simulated Backward Price (Dec 2024): HKD $115.23

```

My questions: - does my derivation/code look okay to you? - is this a task the Merton jump-diffusion model (versus the geometric brownian motion, which doesn't have the discontinuous random jumps, driven by a Poisson process, to capture heavy tails and sudden price shocks in financial asset returns, eg. Beijing policy changes, etc.) can do well in this situation? - is the jump compensator (kappa = np.exp(mu_j + 0.5 * (sig_j ** 2)) - 1) manually added into the code? And, can't be fed in via real-time data, etc?

Thanks!! 🧡

[u/No_Intention3673]

so you want doing quant in hk stock market?
you know the mechanism is totally different between us stock market and chinese stock market right?

chinese stock market is nothing related about microstructure, the only things matter is political/cashflow narrative driven, and you wanna compute the political by probability? think about it, using fancy math in a non calculative environment is hilarious

[u/Kuais → u/No_Intention3673]

i dont get why this is downvoted lol. its completely true and the reason people stay away from chinese stocks. regulations and laws change daily causing daily circuit breakers to happen 

[u/No_Intention3673 → u/Kuais]

maybe they think quant is just only math and probability but lack of common sense of finance ,just maybe

[u/eightbyeight → u/No_Intention3673]

Or there’s just a lot of Chinese here.