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Power producers can exhibit strategic behavior in electricity markets to maximize their profits. This behavior is more pronounced with the deregulation of distribution markets, which offers an opportunity for profit arbitrage between transmission and distribution (T&D) markets. However, the temporally distinct nature of these two markets introduces a significant risk in profit for such producers. This paper derives its motivation from the perspective of a strategic producer and develops a Single Leader Multi-Follower (SLMF) game for deriving its participation strategies in T&D markets, while accounting for different T&D coordination schemes based on the individual market Gate Closure Times (GCT). We compare and contrast joint and sequential market clearing models with regulated and deregulated distribution environments and evaluate the risk of producer by leveraging consistent and coherent risk measures. SLMF game is reformulated as a Mathematical Program with Equilibrium Constraints (MPEC) and is solved using the seminal Scholtes's relaxation scheme. We validate the efficacy of our model and solution approach via the case study carried out on the 11-zone New York ISO, and 7-bus Manhattan power networks, used as transmission and distribution markets, respectively.