#
Incentives for Crypto-Collateralized Digital Assets^{ †}

^{†}

## Abstract

**:**

## 1. Introduction

**Loose price-pegging.**From 2014 to November 2018, the US Dollar-pegged smartcoin BitUSD has maintained an average price near $1, but for extended periods has traded above $1.15, with occasional drops to around $0.90. This is a considerably narrower range than typical freely-floating cryptocurrencies, but stands as an important area for improvement.**Undercollateralization.**To insulate collateral holders from each others’ risky behavior, the MPA system has an in-built safety mechanism known as “global settlement.” In the event of undercollateralization, the global settlement mechanism immediately closes all collateral positions and establishes a fixed exchange rate between BTS and the bitAsset, effectively ceasing any form of price-pegging. This mechanism was triggered in late 2018 on several BitShares-platform smartcoins, including BitUSD (which at the time of writing has a market capitalization of approximately $10 million).

## 2. Model and Performance Metrics

#### 2.1. Collateral Incentive Model

- Core token collateral held by blockchain: Q.
- Stable-token debt: $Q/R$.
- Core tokens held freely: $Q/R$.

#### 2.2. Decision Model

## 3. Our Contributions

#### 3.1. The Interplay between MCR and MSSR

**Proposition 1.**

**Proof.**

**Proposition 2.**

**Proof.**

#### 3.2. Optimal Agent Behavior as a Function of MCR

**Remark 1.**

#### 3.3. Undercollateralization Risk as a Function of MCR

**Remark 2.**

**Remark 3.**

**Remark 4.**

## 4. Discussion and Future Work

- The behavior of token holders may be extremely sensitive to small changes in MCR. This may be exploited to increase liquidity (i.e., by decreasing MCR slightly to incentivize the creation of additional price-stable tokens), but it may be very difficult to predict its precise effects and can easily increase the overall risk in the system.
- The effects of MSSR on token holder behavior may be unintuitive, and essential aspects of their character may be highly dependent on MCR. In our simulations, we found that for low MCR, it is strictly better to set MSSR very close to 1 rather than at a moderate value such as $1.01$, as noted in Remark 4. However, for a somewhat higher MCR, as we note in Remark 3, this situation is reversed and risks decrease with S.

#### Future Work

## Funding

## References

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**2019**, arXiv:1906.02152. [Google Scholar] [CrossRef] - The BitShares Blockchain Foundation. The BitShares Blockchain. Available online: https://www.bitshares.foundation/papers/BitSharesBlockchain.pdf (accessed on 30 June 2019).

**Figure 1.**Plots of agent’s expected profit ratio $P(R;M,S)$ as a function of R for fixed lognormal distribution parameters of $\mu =0.033$ and $\sigma =0.2$, and $S=1.01$ and various values of M. Note that when M is low, e.g., $M=1.4$, the agent’s optimal decision (that is, the maximizer of the corresponding trace on the chart, marked approximately by the red discs) is ${R}^{*}(M,S)=M$. However, increasing M has the tendency to “pull down” the left-hand end of the trace. When $M\approx 1.5$, this gives rise to a local maximum in the profit function away from $R=M$; around $M\approx 1.53$, this local maximum becomes the global maximum and the agent’s optimal collateral ratio “snaps” to the right, yielding ${R}^{*}(M,S)>M$.

**Figure 2.**Plots of system behavior as a function of M for fixed lognormal distribution parameters of $\mu =0.033$ and $\sigma =0.2$ and various values of S. (

**Left**) Agent’s optimal collateral ratio ${R}^{*}(M,S)$ with respect to M. Note that when S is low, the agent’s optimal action is to set $R=M$, but that larger values of S render other, less-risky collateral ratios optimal. (

**Right**) Probability of undercollateralization ${p}_{u}(M,S)$ with respect to M. Several features are of note here: first, when $S=1.02$, the probability of undercollateralization is extremely low, despite the fact that only a $2\%$ penalty is assessed the agent in the event of a margin call. Second, when $S\le 1.01$, the probability of undercollateralization (${p}_{u}$) is sharply dependent on the value of M, can be as high in these simulations as $3.5\%$, and for $S=1.01$, ${p}_{u}$ is discontinuous around $M=1.53$. That is, the probability of undercollateralization is extremely sensitive to the operator’s selection of M.

**Table 1.**Tabular depiction of collateralization incentive model. In the first row, labeled Start, the agent holds Q core blockchain tokens, no debt, and no collateral. In stage 2, the agent has committed Q tokens as collateral and received a loan of $Q/R$ price-stable tokens, which are then sold. In stage 3, the value of the core token has changed by a factor of d; since our accounting is being done in core tokens, the effect of this is that the agent’s debt is modified by a factor of $1/d$. In stage 4, the debt position is closed, resulting in either a profit or a loss for the agent depending on the M and S parameters.

Stage | Debt to Blockchain | Locked Collateral | Freely-Held Tokens |
---|---|---|---|

Start | 0 | 0 | Q |

Position Opened | $\frac{Q}{R}$ | Q | $\frac{Q}{R}$ |

After Price Shock | $\frac{Q}{Rd}$ | Q | $\frac{Q}{R}$ |

Position Closed | 0 | 0 | $P(R,d;M,S)$ Depends on d; see (9) |

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**MDPI and ACS Style**

Brown, P.N.
Incentives for Crypto-Collateralized Digital Assets. *Proceedings* **2019**, *28*, 2.
https://doi.org/10.3390/proceedings2019028002

**AMA Style**

Brown PN.
Incentives for Crypto-Collateralized Digital Assets. *Proceedings*. 2019; 28(1):2.
https://doi.org/10.3390/proceedings2019028002

**Chicago/Turabian Style**

Brown, Philip N.
2019. "Incentives for Crypto-Collateralized Digital Assets" *Proceedings* 28, no. 1: 2.
https://doi.org/10.3390/proceedings2019028002