Climate is an evolving complex system with dynamic interactions and non-linear feedback mechanisms, shaping environmental and socio-economic outcomes. Crop production is highly sensitive to such climatic fluctuations. This paper studies the price volatility of agricultural crops as influenced by meteorological variables (and many other environmental, social and governance factors), which is a critical challenge in sustainable finance, agricultural planning, and policy-making. As case studies, we choose the two Indian states of Madhya Pradesh (for Soybean) and Odisha (for Brinjal). We employ an Exponential Generalized Autoregressive Conditional Heteroskedasticity (EGARCH) model to estimate the conditional volatility of the log returns of crop prices from 2012 to 2024. This study further explores the cross-correlations between volatility and the meteorological variables. Further, a Granger-causality test is carried out to analyze the causal effect of meteorological variables on the price volatility. Finally, the Seasonal Auto-Regressive Integrated Moving Average with Exogenous Regressors (SARIMAX) and Long Short-Term Memory (LSTM) models are implemented as simple machine learning models of price volatility with meteorological factors as exogenous variables. We believe that this will illustrate the usefulness of simple machine learning models in agricultural finance, and help the farmers to make informed decisions by considering climate patterns and making beneficial decisions with regard to crop rotation or allocations. In general, incorporating meteorological factors to assess agricultural performance could help to understand and reduce price volatility and possibly lead to economic stability.